Find f(g(x)) and g(f(x)).
f(x)=x²-2 and g(x)=√x+1

Find F(g(x)) And G(f(x)).f(x)=x-2 And G(x)=x+1

Answers

Answer 1

Answer:

1. x - 1

2. [tex]\sqrt{x^2-1}[/tex]

Step-by-step explanation:

[tex]f(g(x)) = \sqrt{x+1}^2 - 2\\ = x + 1 - 2\\= x - 1[/tex]

[tex]g(f(x)) =\sqrt{x^2-2+1}\\ = \sqrt{x^2-1}[/tex]


Related Questions

A rectangular prism and a cylinder both have a height of 8m, and their cross-sectional areas are equal at every level parallel to their respective bases.

Complete the steps to find the prism.

Answers

1) [tex]V=lwh=5(x)(8)=\boxed{40x}[/tex]

2) [tex]V=\pi r^{2}h=(\pi)(3^{2})(8)=\boxed{72}\pi[/tex]

3) [tex]40x=72\pi\\\\x=\frac{72\pi}{40} \approx \boxed{5.7}[/tex]

f(x) = x² + (k-6) x +9, k * 0. The roots of the equation f(x) = 0 are a and B. (a) Find, in terms of k, the value of (i) a² + ß² (ii) a² ß² Given that 9(a²+ B²) = 2a²p². find the value of k. (b) (c) Using your value of k, and without solving the equation f(x) = 0. form a quadratic equation, with integer coefficients, which has roots and 33² f ( x ) = x² + ( k - 6 ) x +9 , k * 0 . The roots of the equation f ( x ) = 0 are a and B. ( a ) Find , in terms of k , the value of ( i ) a² + ß² ( ii ) a² ß² Given that 9 ( a² + B² ) = 2a²p² . find the value of k . ( b ) ( c ) Using your value of k , and without solving the equation f ( x ) = 0 . form a quadratic equation , with integer coefficients , which has roots and 33²​

Answers

(a) If [tex]\alpha[/tex] and [tex]\beta[/tex] are roots of [tex]f(x)[/tex], then we can factorize [tex]f[/tex] as

[tex]f(x) = x^2 + (k - 6) x + 9 = (x - \alpha) (x - \beta)[/tex]

Expand the right side and match up coefficients:

[tex]x^2 + (k-6) x + 9 = x^2 - (\alpha + \beta) x + \alpha \beta \implies \begin{cases} \alpha + \beta = -(k-6) \\ \alpha \beta = 9 \end{cases}[/tex]

Now, recall that [tex](x+y)^2 = x^2 + 2xy + y^2[/tex]. It follows that

[tex]\boxed{\alpha^2 + \beta^2} = (\alpha + \beta)^2 - 2\alpha\beta = (-(k-6))^2 - 2\times9 = \boxed{k^2 - 12k + 18}[/tex]

and

[tex]\boxed{\alpha^2\beta^2} = 9^2 = \boxed{81}[/tex]

(b) If [tex]9(\alpha^2+\beta^2) = 2\alpha^2\beta^2[/tex], then

[tex]9 (k^2 - 12k + 18) = 2\times81 \implies 9k^2 - 108k = 0 \implies 9k (k - 12) = 0[/tex]

Since [tex]k\neq0[/tex], it follows that [tex]\boxed{k=12}[/tex].

(c) The simplest quadratic expression with roots [tex]\frac1{\alpha^2}[/tex] and [tex]\frac1{\beta^2}[/tex] is

[tex]\left(x - \dfrac1{\alpha^2}\right) \left(x - \dfrac1{\beta^2}\right)[/tex]

which expands to

[tex]x^2 - \left(\dfrac1{\alpha^2} + \dfrac1{\beta^2}\right) x + \dfrac1{\alpha^2\beta^2}[/tex]

Reusing the identity from (a-i) and the result from part (b), we have

[tex]\left(\dfrac1\alpha + \dfrac1\beta\right)^2 = \dfrac1{\alpha^2} + \dfrac2{\alpha\beta} + \dfrac1{\beta^2} \\\\ \implies \dfrac1{\alpha^2} + \dfrac1{\beta^2} = \left(\dfrac{\alpha + \beta}{\alpha\beta}\right)^2 - \dfrac2{\alpha\beta} = \left(\dfrac{-(k-6)}9\right)^2 - \dfrac29 = \dfrac29[/tex]

We also know from part (a-ii) that [tex]\alpha^2\beta^2=81[/tex].

So, the simplest quadratic that fits the description is

[tex]x^2 - \dfrac29 x + \dfrac1{81}[/tex]

To get one with integer coefficients, we multiply the whole expression by 81 to get [tex]\boxed{81x^2 - 18x + 1}[/tex].

What is the y-intercept of this quadratic function f(I)=-i2+10i-22

Answers

The y-intercept of the quadratic equation is -47.

What is Quadratic Equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Here, given quadratic equation;

    f(i) = i² + 10i - 22

or, y = i² + 10i - 22

     y = i² + 2.5x - (47-25)    

    y = i² + 2.5x + 25 - 47

    y = (i+5)² - 47

Thus, the y-intercept of the quadratic equation is -47.

Learn more about Quadratic Equations from:

https://brainly.com/question/2263981

#SPJ1

Rick bought some tetra fish and goldfish for his fish tank. He bought twice as many goldfish as he did tetras. Each goldfish costs $1.50, and each tetra fish costs $2.00. He spent $20 on the fish. Which system can be used to represent x, the number of tetra fish, and y, the number of goldfish, he purchased?
x = 2 y. 2 x + 1.5 y = 20
2 x = y. 2 x + 1.5 y = 20
x = y. 2 x + 1.5 y = 20
x + y = 20. 2 x + 1.5 y

Answers

Answer:

  B.  2x = y; 2x +1.5y = 20

Step-by-step explanation:

The two given relations can be written as two equations, one for the numbers of fish, and one for their cost.

__

number of fish

The number of goldfish (y) is twice the number of tetras (x), so one equation can be ...

  2x = y

cost of fish

The tetras (x) are $2 each, and the goldfish (y) are $1.50 each. Their total cost is the sum of products of the number of fish and the cost of each. That total is given as $20, so the other equation could be ...

  2x +1.5y = 20

Then the appropriate system of equations is ...

2x = y2x +1.5y = 20

_____

Additional comment

The solution can be found by substituting for 2x to get ...

  y +1.5y = 20 . . . . . . substitute for 2x

  y = 20/2.5 = 8 . . . . divide by the coefficient of y

  x = y/2 = 4 . . . . . . . find the number of tetras

Rick bought 4 tetras and 8 goldfish.

__

The wording "twice as many goldfish as tetras" easily causes confusion. It is helpful to reword it as "goldfish were twice the number of tetras."

Can someone help me find AB and BC

Answers

3x + 2x + 5 + 5x + 15 = 180 [angles on a line add to 180 degrees]10x + 20 = 180 [combine like terms]10x = 160 [subtract 20 from both sides]x = 16 [divide both sides by 10]

Arc AB measures 3(16) = 48 degrees.

Arc BC measures 2(16) + 5 = 41 degrees.

A pyramid has a square base with sides of length s. The height of the pyramid is equal to 1/2 of the length of a side on the base. Which formula
represents the volume of the pyramid?
A. V = 1/12 s ^3
B. V=1/6 s ^3
C. V=1/3s ^3
D. V=3s³
E. V=6s³

Answers

Answer:

The volume of the pyramid with a base area of s² and the heights iss

The formula for calculating the volume of a square based pyramid is expressed as:

Volume = 1/3* Base area* Height

Since it is a square-based pyramid, the base area is calculated as:

Base Area = s ^ 2

If the height of the pyramid is equal to of the length of a side on the base, hence h = s

Substituting the base area and the height into the formula for the volume, this will give;

V = BH / 3

V = (s ^ 2 * s)/3

V = (s ^ 3)/3

V = 1/3 * s ^ 3

Hence the volume of the pyramid with a base area of s ^ 2 and the height s is 1/3 * s ^ 3

Which equation has x-intercepts located at (-1,0) and (-5,0)?
A. y=(x + 1)(x - 5)
B. y=(x + 1)(x + 5)
C. y=(x-1)(x - 5)
D. y=(x-1)(x + 5)

Answers

Answer:

B. y = (x+1)(x+5)

Step-by-step explanation:

If the x-intercepts are (-1,0) and (-5,0), then the solutions (also called zeros and x-intercepts) are

x = -1 and x = -5

This is a "working backwards" kind of problem. If you were solving the equation, right before the final step, x=-1 would have been:

x + 1 = 0

Right before x=-5

would have been,

x + 5 = 0.

These two: x+1 and x+5 are called the linear factors. You multiply them back together to find the equation.

y = (x+1)(x+5)

A cell phone towerbcast a shadow that is 40 feet long . An 10- foot- tall stop sign located near the tower casts a shadow that is 8 feet long. How tall is the cell phone tower?

Answers

Using proportions, considering the relation between the height and the shadow, it is found that the cell phone tower is 50 feet.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

When the shadow is of 8 feet, the height is of 10 feet. What is the height when the shadow is of 40 feet? The rule of three is:

8 feet - 10 feet

40 feet - h feet

Applying cross multiplication:

8h = 10 x 40

Simplifying by 8:

h = 10 x 5 = 50 feet.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Which of the following is a geometric sequence?
• A. 6, 18, 54, 162
O B. 1, 4, 5, 9, 14
O C. 3, 6, 9, 12, 15
O D. 3, 5, 8, 13, 21

Answers

Answer: A. 6, 18, 54, 162

Step-by-step explanation:

Each term is 3 times the last, meaning the common ratio is 3.

What are the values for y when x is 2, 4, and 6?
y = 20x + 7

Answers

Wait what’s the value of x?
When x is 2 y=40+7 = 47
When x is 4 y= 80+7 =87
When x is 6 y= 120+7 =127

find the missing number in ?/4 = 27/36​

Answers

[tex]\text{First I would recommend replacing the question mark with x}\\\text{We have two ratios, }\\\text{and we need to solve that hard-looking equation}\\\text{in terms of x}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{We can multiply x times 36:: 36x}\\\text{We can multiply 4 times 27:: 108}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{Now it's easier to solve for x:: 36x=108; x=3}\\\text{ (we divided by 36 on both sides of the = sign)}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{The missing number is 3}[/tex]

find the value of x

d:6​

Answers

[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve for x ~

[tex]\qquad \sf  \dashrightarrow \: 5x = 3x + 12[/tex]

[ by vertical opposite angle pair ]

[tex]\qquad \sf  \dashrightarrow \: 5x - 3x = 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x = 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 12 \div 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 6[/tex]

Therefore, the correct choice is D. 6

Answer: D) 6

Step-by-Step Solution:

We know, (5x)° and (3x + 12)° are Vertically Opposite Angles and Vertically Opposite Angles are Equal.

Therefore,
5x = 3x + 12
5x - 3x = 12
2x = 12
x = 12/2
=> x = 6

Therefore, x = 6

Help me with this question please and thank you!! :)

Answers

[tex]A \cup B[/tex] represents the set that contains all the elements that are in at least one of the sets, so [tex]A \cup B=\{1, 2, 5, 6, 7, 8, 9, 10, 12, 16, 18, 19, 20, 21, 22, 23, 25\}[/tex].

We want the complement of this set (in other words, the set with all the elements in the universal set but not in the given set).

This set is {3, 4, 11, 13, 14, 15, 17, 24}

After 8 points are added to each score in a sample.
the mean is found to be M = 40. What was the
value for the original mean?

Answers

I think it’s 32 because it’s more simple then it looks! It would just be 40-8??

please help me :((((((

Answers

Answer:

Answer D

Step-by-step explanation:

It says to divide f(x)/g(x), which is displayed in D and if we find the domain it would be x is not equal to -1/4

What is the range of y=sin(x)?

Answers

The range of y = sin(x) is [-1,1]

How to determine the range?

The function is given as:

y = sin(x)

The above function is the parent function of a sine function.

A sine function has a minimum of -1 and a maximum of 1.

This is represented by the interval [-1,1]

Hence, the range of y = sin(x) is [-1,1]

Read more about range at:

https://brainly.com/question/10197594

#SPJ1

The sequence an = 1(3)n − 1 is graphed below: coordinate plane showing the points 1, 1; 2, 3; and 3, 9 Find the average rate of change between n = 1 and n = 3. (6 points)

Answers

Answer:

4

Step-by-step explanation:

[tex] \frac{9 - 1}{3 - 1} = 4[/tex]

The average rate of change on the interval [3, 9] will be 4.

How to find the average rate of change?

The average rate of change between two points is given by the slope formula:

 m = average rate of change = (y2 -y1)/(x2 -x1)

The sequence an = 1(3)n − 1 is graphed below:

 m = (9 -1)/(3 -1) = 8/2

 m = 4

The average rate of change on the interval [3, 9] will be 4.

Learn more about average rate;

https://brainly.com/question/12395856

#SPJ1

the height of a toy rocket

Answers

16t2 + 48tf = 16t2 + 48t

The second one is the answer

Q6. This part of the question is for simplifying your work: Make a graph and shadow the interested regions of the inequalities in the given picture.
The following is the actual question: Find the highest and lowest value of the equation in the given picture within the unshadowed region.

Answers

The graph of all the inequalities are given below.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign.

This part of the question is for simplifying your work: Make a graph and shadow the interested regions of the inequalities in the given picture.

y ≥ x, the region is left to the line.

y < -(3/7)x – 7, the region is left to the line.

y ≤ (5/3)x – 8, the region is right to the line.

y ≥ 14 – (11/12)x, the region is right to the line.

y = -(3/2)x + 5, this is the equation of line.

All the graphs are shown below.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ1

Item 6
A set of books sits on a shelf at a store. This line plot shows the thickness of each book. Juan buys one of the thickest books on the shelf. Min buys the third thinnest book on the shelf.

How much thicker is Juan’s book than Min’s book?

Answers

Answer:

There is no line plot

Step-by-step explanation:

2 and a half(what’s ever size it’s in) I had this question today! Pretty sure there the same but not 100%

1 x 1 x 99 x 100 hat is the awnser

Answers

The answer to this equation is 9,900. Why? Well, we can solve this equation in left-to-right format, seeing that there are no brackets, exponents, or parenthesis:

Step One: 1 x 1 = 1. Anything multiplied by one is the same number that was started with.

Step Two: 1 x 99 = 99. Again, anything multiplied by one is the same number that we started with, which in this case was 99.

Step Three: 99 x 100 = 9,900. Because 100 is a power of ten, we could easily find the solution by shifting the digits two places to the left to increase their value. However, if you would like to do it the long way, you could simply write out 100 x 99 and solve it.

Your final answer: 1 x 1 x 99 x 100 = 9,900.

Find f(g(3)) and g(f(-2)).
f(x)=x²-1 and g(x)=2x-3

Answers

Answer:

1. 8

2. 3

Step-by-step explanation:

[tex]f(g(3)) \\= f(2(3)-3))\\=f(3)\\=3^2-1\\= 9-1\\=8\\\\g(f(-2))\\= g((-2)^2-1)\\=g(4-1)\\=g(3)\\=2*3-3\\=3[/tex]

if n × 18 = ½ find n

Answers

n=1/2/18
n=1/2 multiplied 1/18
n=1/36

Answer:

n = [tex]\frac{1}{36}[/tex]

Step-by-step explanation:

n × 18 = [tex]\frac{1}{2}[/tex]

To find the value of n we have to divide both sides by 18.

Let us solve it now.

18n = [tex]\frac{1}{2}[/tex]

[tex]\frac{18n}{18}[/tex] = [tex]\frac{1}{2}[/tex] ÷ 18

n =  [tex]\frac{1}{2}[/tex] ÷ 18

n = [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{18}{1}[/tex]

n =  [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{18}[/tex]

n = [tex]\frac{1}{36}[/tex]

The graph of y = is reflected over the y-axis and then translated down 2 units to form f(x). Which is the graph of f(x)?

Answers

If the function is reflected over the y-axis and then translated down 2 units. the resulting function will be -∛x - 2

Transformation of coordinates

Transformation is a technique used to change the position of an object on an xy-plane.

Given the function y = ∛x

If the function is reflected over the y-axis and then translated down 2 units to form f(x), the resulting function f(x) will be:

f(x) = -∛x - 2

The graph of the resulting function is attached

Learn more on translation here: https://brainly.com/question/12861087

#SPJ1

Answer:

B

Edge 2023

The other answer is incorrect!!!

An object is dropped from 39 feet below the tip of the pinnacle atop a ​715-ft tall building. The height of the object after seconds is given by the equation . h=16T^2+676.Find how many seconds pass before the object reaches the ground.

Answers

Answer:

6.5 seconds

Step-by-step explanation:

Ok so the equation you gave is -16T^2 + 676 in the comments which is what I'll be using for this problem. The problem is really just asking you to find the zeroes of the equation excluding any negative solutions since that doesn't really represent anything in this context since T is time.

So the first step is to set the equation equal to 0

[tex]0 = -16t^2 + 676[/tex].

Subtract 676 from both equations.

[tex]-676 = -16t^2[/tex]

Divide both sides by -16

[tex]42.25 = t^2[/tex]

Take the square root of both sides

[tex]\pm6.5 = t[/tex]

Ignore the negative and take only the positive solution, since in this context it doesn't make much sense. So after 6.5 seconds the height is 0, meaning it hits the ground after 6.5 seconds.

Write an equation for the transformed logarithm shown below, that passes through (-2,0) and (0,-3)

Answers

Using translation concepts, the equation for the transformed logarithm is given by:

[tex]f(x) = \log{(x + 3)} - 3.48[/tex]

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The logarithm function is given by:

[tex]f(x) = \log{x}[/tex].

We have that:

It passes through (1,0), and in this problem it passes through (-2,0), that is, it was shifted left 3 units, hence x -> x + 3.

Hence:

[tex]f(x) = \log{x + 3} + b[/tex]

To find the shift up/down, we consider that f(0) = -3, hence:

[tex]-3 = \log{0 + 3} + b[/tex]

[tex]b = -3 - \log{3}[/tex]

b = -3.48.

Hence the function is given by:

[tex]f(x) = \log{x + 3} - 3.48[/tex]

More can be learned about translation concepts at https://brainly.com/question/4521517

#SPJ1

If f(x) = 3x − 1 and g(x) = x + 2, find (ƒ– g)(x) ​

Answers

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:2x - 3 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: (f - g)(x)[/tex]

[tex]\qquad \tt \rightarrow \: f(x) - g(x)[/tex]

Simple procedure :

[tex]\qquad \tt \rightarrow \: 3x - 1 - (x + 2)[/tex]

[tex]\qquad \tt \rightarrow \: 3x - 1 - x - 2[/tex]

[tex]\qquad \tt \rightarrow \: 3x - x - 1 - 2[/tex]

[tex]\qquad \tt \rightarrow \: 2x - 3[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

I’m going to need a serious answer through this one or I’m screwed.

Answers

Answer:

A = 60 ft²

Step-by-step explanation:

the area (A) of the shaded sector is calculated as

A = area of circle × fraction of circle

   = 90 × [tex]\frac{240}{360}[/tex]

   = 90 × [tex]\frac{2}{3}[/tex]

    = 30 × 2

    = 60 ft²

Answer:

58.83 ft^2

Step-by-step explanation:

Finding the radius:

A = πr^2

90 = πr^2

90/π = r^2

28.6 = r^2

5.3 = r

Using the area of a sector of a circle formula:

θ/360 x πr^2

240/360 x π(5.3)^2

= 58.83 ft^2

What are the measures of ∠1 and ∠2? Show your work or explain your answers.

Answers

Answer:

angle 1 is 105degrees and angle 2 is 75degrees

Step-by-step explanation:

The angle below angle 2, presumably angle 6, is also 75 degrees since line c and line d are parallel. If angle 2 is 75 degrees then we know that angle 1 is 105 degrees since both angles equal a straight line and a straight line has 180 degrees.

what is 2/3 x 6/7 answer

Answers

Answer:

4/7

Step-by-step explanation:

2/3 × 6

7

4/7

and bro that's really it

Other Questions
Which of the following would cause an increase in the magnetic forcebetween two magnets?A. Decreasing the separation between the two magnetsB. Increasing the separation between the two magnetsC. Decreasing the amount of excess charge on the first magnetD. Increasing the amount of excess charge on the first magnet A section of DNA is shown. 3'TCG ATA TCC5' Which sequence best shows the result of transcription for the section of DNA?A. AGC TAT AGGB. TCG ATA TCCC. UCG AUA UCCD. AGC UAU AGG What is the density of the oak board A point located on the second hand of a large clock has a radial acceleration of 0. 1cm/s2. How far is the point from the axis of rotation of the second hand? Assume that real gdp has been declining and the unemployment rate has been edging upward. What might the congress and the president do about this problem? Triangle abc is represented. points d and f are marked on side ab and points e and g are marked on side ac. segments de and fg are drawn. if , then line segment is parallel to line segment . how does the media expose human rights violation HELPPPPPPPPP IMMEDIATELY 32 out of 40 kids said they prefer summer over winter. 25 out of 32 adults said they prefer summer. Did a larger percentage of kids or adults prefer summer. A quarter weighs the same as two pennies. If a pound of quarters is worth $25, then how much is a pound of pennies worth? Question 7 of 10The description below is about a community in a poor country in need ofcertain basic necessities.A village is without electricity and running water but is far from the ocean in awarm climate. Food is limited and farming is close to non-existent becausethere is no access to a water supply. The only nearby water is deepunderground.Given the problems of the village, which technology is best for quicklyimproving its carrying capacity?A. Building a plant that takes salt out of waterOB. Drilling for waterOC. Designing a plant that uses water to make electricityOD. Farming using vertical buildings4SUBMIT Why is the word yet powerful in developing a growth mindset?. PLEASE help me in this subject omg is hard I will five u points I promise The y-intercept of the line whose equation is 2x - 3y = 6 is -2 3 6 Relevant facts relate to the topic andaddress the counterclaim to an argument.give evidence to support reasons in an argument.connect ideas clearly and logically.provide an essay with a strong conclusion. Janelle is painting a spherical model of a human cell for a science fair. She uses 615.44 square inches of paint toevenly cover the outside of the cell with one coat of paint. What is the diameter of the cell model? (Use 3.14 for thevalue of n.)7 in.8 in.14in16in Which best summarizes the flow of energy in a producer?O Sun > ADP > muscle cellsO Sun > mitochondria > CoH1206O Sun > chloroplasts > mitochondriaO Sun > mitochondria > chloroplasts which statement is correct? A triangle with side lengths a, b, and c is shown below.Which statement about the side lengths must be true?A a+b>cB b+cC a+bD a+c An employee earned $61,300 during the year working for an employer. The Federal Insurance Contributions Act (FICA) tax rate for Social Security is 6.2% of the first $137,700 of employee earnings per calendar year, and the Federal Insurance Contributions Act (FICA) tax rate for Medicare is 1.45% of all earnings. The current Federal Unemployment Taxes (FUTA) tax rate is 0.6%, and the State Unemployment Taxes (SUTA) tax rate is 5.4%. Both unemployment taxes are applied to the first $7,000 of an employees pay. What is the amount of total unemployment taxes the employee must pay?