Given f(x)=x−1−−−−√+2, what is the relationship between f(x) and f−1(x)? Drag and drop an inequality into each box to correctly complete each statement.
Answers
Answer:
The domain of f(x) is x>-2, so the range of f-1(x) is y>-2
The range of f(x) is y>-1, so the domain of the f-1(x) is x>-1
Step-by-step explanation:
To solve this question, we need to know the definition of domain and range.
The domain of a function is defined as all the possible input x-values while the range is defined as all the possible output y-values.
For f(x), domain for x is; x ≥ 1 and range is; y ≥ 2
For f⁻¹(x); domain is; x ≥ 2 and range is; x ≥ 1
We are given the function;
f(x) = [tex](\sqrt{x - 1} ) + 2[/tex]
Now, when x = 1, we will have zero inside the square root sign and this means that any x-value less than 1 will make the value inside the square root symbol to be negative which will result in an imaginary root.
Thus, we can say that, the domain for x is; x ≥ 1
Putting x = 1, we can find the least range value;
f(x) = 0 + 2
f(x) = 2
Thus, the range will be; y ≥ 2
Now, we want to find the range of f⁻¹(x)
This means an inverse of the original equation.
Thus;
f⁻¹(x) = [tex](x - 2)^{2} + 1[/tex]
Let's put x = 2;
f⁻¹(x) = (2 -2)² + 1
f⁻¹(x) = 1
Since x=2 gives the bracket to be zero, it means the domain is; x ≥ 2 and range is; x ≥ 1
Read more at; brainly.com/question/24522291
Related Questions
Solve the inequality. Graph the solution.
|6x - 3| + 5 < 20
Can someone help please show the work for it please thanks
Answers
What is the square of 3?
12
9
27
6
15
Answers
-1.4(-5+7g)=? simplify the expression
Answers
Answer:
7 - 9.8g
Step-by-step explanation:
[tex]-1.4(-5+7g)\\\\\boxed{7-9.8g}\\\\\left \{ {{-1.4*-5=7} \atop {-1.4*7g=-9.8g}} \right.[/tex]
Hope this helps.
The simplified form of the expression will be 7-9.8g.
What is a mathematical expression?A mathematical expression is a sentence that has at least two variables or integers and one mathematical action. In mathematics, it is possible to multiply, divide, add, or subtract. The construction of an expression is as follows: Expression, number, and mathematical operator.
It is given that the expression is,-1.4(-5+7g
We have to simplify the expression.
Suppose the simplified value of the expression is x,
x= -1.4(-5+7g)
x= -1.4(-5)-1.4(7g)
x=7-9.8g
Thus the simplification of the expression will be 7-9.8g.
Learn more about the expression here:
brainly.com/question/14083225
#SPJ2
Which expressions are equivalent to 4 (4a + 5) ?
Answers
Answer:
16a+20
Step-by-step explanation:
Distribution property
4×4a + 4×5
16a. + 20
∠3 and ∠4 are supplementary angles. Given m∠3=116°, find m∠4. m∠4= °
Answers
Supplementary angles are angles that add up to 180 degrees.
m<3 + m<4 = 180 degrees
116 + m<4 = 180 degrees.
Subtract 116 from both sides.
m<4 = 64 degrees
The value of ∠4 will be 64°.
It is given that ∠3 and ∠4 are two supplementary angles.
We have to find out the value of ∠4 , if ∠3 = 116 °.
What are the supplementary angles ?
Supplementary angles are angles that add up to 180 degrees.
As per the question ;
∠3 and ∠4 are supplementary angles.
We know that sum of supplementary angles is 180° .
⇒ ∠3 + ∠4 = 180°
given ; ∠3 = 116°
⇒ 116° + ∠4 = 180°
⇒ ∠4 = 180° - 116°
⇒ ∠4 = 64°
Thus , the value of ∠4 will be 64°.
To learn more about supplementary angles click here ;
https://brainly.com/question/22604713
#SPJ2
Solve the equation below for x: - 3/ x+2 = 7 /x+5
Answers
Answer:
X = -29/10
Step-by-step explanation:
Solve for x. 3 − 3/4 x = 1/4 x − 7
A) −10
B) −4
C) 4
D) 10
Answers
Answer:
x = 10
Step-by-step explanation:
[tex]3 - \frac{3}{4}x = \frac{1}{4}x - 7[/tex]
Start by subtracting 3 to both sides
[tex]-\frac{3}{4}x = \frac{1}{4}x-10[/tex]
Subtract 1/4x from both sides ( -3/4 - 1/4 ) = - 1
[tex]-x = -10[/tex]
Divide both sides by a negativ 1 to get rid of the negative
∴ [tex]x = 10[/tex]
Simplify the expression 4a − 5b − 6 + 2b − 3a.
Answers
Answer:
a-3b-6
Step-by-step explanation:
(4a-3a)(-5b+2b)(-6)
a-3b-6
The club supplies 40 new balls for each player which cost $1 each. Each player pays $300 for the lessons. The club must pay each instructor $1,000 for conducting the lessons, and there must be at least 1 instructor for every 6 players. Which amount of players and instructors meets these requirements and still gives the club a net profit?
6 players and 2 instructors
10 players and 3 instructors
13 players and 2 instructors
16 players and 3 instructors
Answers
Answer: D.) 16 players and 3 instructors
Step-by-step explanation:
Just took the quiz;)
what is 24/98 in simplest form
Answers
Answer:24 ÷ 2
98 ÷ 2
Reduced fraction:
12
49
Therefore, 24/98 simplified to lowest terms is 12/49.
Step-by-step explanation:
A speed walker covered 4 1/2 mi in 3/4 hour. How far will he walk in 3/4 hours if he walks twice as fast?
PLS HELP ASAP
Answers
Answer: 9 miles
Step-by-step explanation:
The distance would be 9 because if the speed walker walked 4.5 miles in 3/4 of an hour, he would be going 6 mph (miles per hour).
If he walks twice as fast, he would be going 12 mph.
If he walks for 3/4 of an hour (45 minutes) at 12 mph, he would walk 9 miles.
9 miles he walks in 3/4 hours if he walks twice as fast.
What is speed?Speed is characterized as the pace of progress of the position of an item toward any path. Speed is estimated as the balance of length to the time in which the distance was covered. Speed is a scalar amount as it has just course and no size.
4 1/2 miles will be covered by him in 3/4 hour
if the speed walker covered 4.5 miles in just over an hour
The duration would indeed be 9 since the speed walker might be moving at a rate of six miles per hour.
He would be moving at 12 miles per hour if he walked twice as quickly.
He would cover 9 miles in 3/4 of an hour (45 minutes) of walking at a speed of 12 miles per hour.
Learn more about speed, here:
https://brainly.com/question/28224010
#SPJ3
What is the answer to this?
Answers
Answer:
[tex]\huge\boxed{-6}[/tex]
Step-by-step explanation:
Since we know the values of a, b, and c, we can substitute them into our expression and get the value.
[tex]-2b + | -3c + a |\\\\-2(6) + |-3(-3) + -3 |[/tex]
A negative multiplied by a negative gets us a positive.
[tex]-2(6) + |9 + -3 |[/tex]
Adding a negative is the same as subtracting a positive.
[tex]-2(6) + |9 -3 |\\-2(6) + 6[/tex]
[tex]-2 \cdot 6 = -12\\\\-12+6\\\\-6[/tex]
Hope this helped!
Change the value of n some more, and observe how the lengths of the sides of the image change. Once you've settled on a value for n, record it in the table. Measure the lengths of the sides on . Do this for at least three different values of n. What is the relationship between the lengths of the sides of and ? Explain the relationship in terms of n.
Answers
Answer:
n=3.5 a=1.41 units a'=4.95 units b3 units b'10.5 units c2.24 units c'=7.83 units
Step-by-step explanation:
This answer assumes that n = 3.5. The ratio of each side length on to the corresponding side length on is equal to 3.5. For example, a′ = 3.5a. The ratio is equal to the scale factor, n.
What number makes the equation true? Enter the answer in the box. 5 = 45 ÷
Answers
Answer:
9
Step-by-step explanation:
Answer:
The answer is 9
Step-by-step explanation:
The answer is 9 because 9*5=45
What are the exponents
A^m * A^n =
Answers
Answer:
A ^ ( m+n)
Step-by-step explanation:
When we are multiplying terms with exponents and the bases are the same, we can add the exponents
A^m * A^n =
A ^ ( m+n)
Answer:
m and n
Step-by-step explanation:
Exponents are the raised numbers or letters.
So it is m and n
In an ap if a=-15,an=1 and sun=-63 then n is
Answers
Step-by-step explanation:
n=an-a
n=1--15
n=16
this might be helpful for you of it isnt I am super sorry
What is the solution for x in 12x - 4 = 5x + 24?
Answers
Answer:
x=4
Step-by-step explanation:
Add 4 to both sides.
12x=5x+24+4
Simplify 5x+24+4 to 5x+28
Subtract 5x from both sides
12x-5x=28
Simplify 12x-5x1 to 7x
7x=28
Divide both sides by 7
28/7
simplify 28/7
x=4
Answer:
4
Step-by-step explanation:
12x - 4 = 5x + 24 convert like terms to the same side of equation
12x - 5x = 24 + 4 as you can see, when we send a terms to the other side of equation its sign changes
7x = 28 multiply both sides by 7
x = 4
X X 7
What is the solution to the equation 3+6 - 2?
?
3
x = 2
7
O x = 3
0x = 3
x = 7
Answers
Answer:7
Step-by-step explanation:
The solution to the equation 3 + 6 - 2 is 7.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We also find the solution in a system of equations using the substitution or elimination method.
Example:
2x + 4 = 8
The solution is x = 2.
We have,
The given equation is 3 + 6 - 2
Simplifying the terms inside the parentheses first.
= 9 - 2
= 7
Therefore,
The solution to the equation 3 + 6 - 2 is 7.
Learn more about solutions of equations here:
https://brainly.com/question/545403
#SPJ7
scores on the act college entrance exam follow a bell-shaped distribution with mean 18 and standard deviation 6. Wayne's standardized score on the ACT was -0.5. what was Wayne's actual ACT score?
Answers
Answer:
His actual score is 15
Step-by-step explanation:
Here, we are interested in calculating Wayne’s actual score on the ACT
when we say the scores have being standardized, it means the score was reported in terms of the z-score and not the initial raw scores.
Now, mathematically, for the scores to have a negative z-score, it means it is actually below the mean.
The formula for the z-score or standard score is given below;
z-score = (x - mean)/SD
where in this case, x = ? which is the score we are looking for , z-score = -0.5 , mean score = 18 and standard deviation of the scores = 6
So, substituting these values into the z-score equation, we have;
-0.5 = (x-18)/6
x-18 = 6(-0.5)
x -18 = -3
x = -3 + 18
x = 15
Simplify (5x−2+3x^2)+(4x+3)
Answers
Answer:
3x^2 + 9x + 1
Or
3x ( x + 3 ) + 1
Step-by-step explanation:
(5x - 2 +3x^2 ) + (4x + 3 )
To make this a little bit more easier to read, you can remove the parentheses:
5x - 2 + 3x^2 + 4x + 3
Now, write in a way so that the like terms are next to each other:
3x^2 + 5x + 4x - 2 + 3
Now simplify the 'x' terms to get:
3x^2 + 9x - 2 + 3
Now, simplify the integers (the ones with now variables with them) to get:
3x^2 + 9x + 1
If you want, you can factor out the 3x for two of the terms to get :
3x ( x + 3 ) + 1
Therefore, your simplest form can either be 3x^2 + 9x + 1 OR 3x (x + 3 ) + 1
Help with the question above please????
Answers
Which of the following inequalities have no solution over all real numbers? Check all that apply.
Answers
Answer:
cos(x)<-2
-1<csc(x)<1
cos(x)-1>.5
Step-by-step explanation:
I just answered this question and got these answers.
Answer:
a d e
Step-by-step explanation:
edge 2020
Find the unit rate of 750 yards in 25 min?
Answers
Answer:
750 yards/25 minutes = 30 yards per minute
Step-by-step explanation:
Answer : If you divide both numbers the answer will be it for 1 minute so the answer to this question is 30 yards
Answer: 30 yards per minute
Step-by-step explanation:
750/25
30
Two lines intersect at exactly 1 point
O Sometimes
O Always
O Never
Answers
Which of the following numbers can be a
solution to the inequality for number 2?
2x - 15 < -23
(Check ALL that apply)
-7
-4
3
4
Answers
2x - 15 < -23
Add both sides by 15:
2x < -8
Divide both sides by 2:
x < -4
Answer: -7 is the only one that satisfies the condition
complete the square
x2×7x+
Answers
Answer:
49
Step-by-step explanation:
True or false Exterior angles are the angles created when the sides of the triangle are shortened.
This statement is true.
This statement is false. Exterior angles are pairs of angles whose measures add up to 360
This statement is false. Exterior angles are the angles inside the triangle
This statement is false. Exterior angles are the angles created when the sides of the triangle are extended.
Answers
Answer:
The statement is false. Exterior angles are the angles created when the sides of the triangle are extended
Step-by-step explanation:
In order to find the exterior angle of a polygon, the side of the polygon is extended to go past the vertex of the polygon to form an angle adjacent and supplementary to the the interior angle of the polygon at the vertex of the polygon where the exterior angle is formed.
The sum of the exterior angle and the adjacent interior angle is equal to 180°
The exterior angle can also be described as being formed by one side of a polygon and an extension of the adjacent side to previous side of the same polygon and it can also be referred to as a turning or an external angle.
What is the value of x3 + x2 + when x=3
Answers
(3)(3)=9
(3)(2)=6
9+6= 15
The image point of A after a translation left 3 units and down 1 unit is the point
B(-8, -2). Determine the coordinates of the pre-image point A.
Answers
Answer:
b
Step-by-step explanation:
There is no answer or document
The coordinates of the pre-image of point A are (-5, -1).
What is the difference between upward, downward, leftwards and rightwards translation?Upward translation = [k] units
When the upward translation take's place then, each point will have its y - coordinate shifted upwards by +k units.
Downward translation = [k] units
When the downward translation will take place then, each point will have its y - coordinate shifted downwards by -k units.
Leftward Translation = [k] units
When the leftward translation will take place then, each point will have its x - coordinate shifted by -k units to the left.
Rightward Translation = [k] units
When the rightward translation will take place then, each point will have its x - coordinate shifted by +k units to the right
We have the image of point [A] after a translation left by 3 units and down by 1 unit is the point B(-8, -2).
Assume that the original coordinates are -
(x, y)
Then, we can write -
(x - 3, y - 1) = (-8, -2)
x - 3 = - 8
y - 1 = -2
x = - 5
y = - 1
Therefore, the coordinates of the pre-image of point A are (-5, -1).
To solve more questions on Graph translations, visit the link below -
brainly.com/question/12802031
#SPJ2
Try to solve (-78)+43 #
Answers
Answer:
-35
Step-by-step explanation:
you put -78 on top and take put 43 the put the negative back on
Answer:
-35
Step-by-step explanation:
negative + positive = negative
