Function Inverses

Which ordered pair is on the inverse of f(x)?

(-1, -2)

f−1(−2) = f(−4) = f(f−1(−2)) =

1) -4 2) -2 3) -2

Use f(x) = 1/2x and f^-1(x) = 2x to solve the problems. f(2) = f−1(1) = f−1(f(2)) =

1) 1 2) 2 3) 2

Find the inverse of each of the given functions. f(x) = 4x − 12 f−1(x) = __________ x + __________

1) 1/4 2) 3

The inverse of F(C) = 9/5C + 32 is C(F) = F −

1) 5/9 2) 160/9

The rule that maps each domain value to its range value is f(x) = __________x.

1/2

Check all that apply.

F is a function. F is a one-to-one function. C is a function. C is a one-to-one function.

Waterloo Park posted the following schedule listing the number of hours an employee works on a given day. Let B(x), T(x), R(x), and S(x) represent the number of hours worked by Bill, Ted, Rufus, and Socrates, respectively, on a given day x. What is the value of the inverse shown below? S -1 (0) =

Friday

Which graphs are inverses of one another?

Graph A and C

Talib is trying to find the inverse of the function to the right. His work appears beneath it. Is his work correct? Explain your answer.

His work is not correct. You first must switch x and y and then solve for y.

Is the inverse of the function shown below also a function? Explain your answer.

If the graph passes the horizontal-line test, then the function is one-to-one. Functions that are one-to-one have inverses that are also functions. Therefore, the inverse is a function.

Danika concludes that the following functions are inverses of each other because f(g(x)) = x. Do you agree with Danika? Explain your reasoning. f(x) = |x| g(x) = -x

She is not correct. She forgot to do g compose f. To verify that functions are inverses of each other, you must also show that g(f(x)) = x. Because g(f(x)) = -x, the functions are not inverses of each other.

Find the values of a through e that make these two relations inverses of each other. a = b = c = d = e =

a = -3.8 b = -2.6 c = 1.7 d = 4.4 e = 1

Sample Response: If the graph passes the horizontal-line test, then the function is one-to-one. Functions that are one-to-one have inverses that are also functions. Therefore, the inverse is a function. Compare your response to the sample response above. What did you include in your explanation?

a reference to the horizontal-line test a statement that the function is one-to-one the conclusion that the inverse is a function

The range values of an inverse are the __________ values of the original function.

domain

Select each pair of functions that are inverses of each other.

f(x) = {(-5,-9), (-3,-4), (0,1), (3,7), (6,13)} g(x) = {(-9,-5), (-4,-3), (1,0), (7,3), (13,6)} f(x) = x + 7; g(x) = x - 7

Select the equation that is the inverse of the given function. f(x) = x-3/5

f^-1(x) = 5x + 3

Select each graph that shows a function and its inverse.

first and fourth

Identify the inverse g(x) of the given relation f(x). f(x) = {(8, 3), (4, 1), (0, -1), (-4, -3)}

g(x) = {(3, 8), (1, 4), (-1, 0), (-3, -4)}

Choose a true statement.

g(x) is a function because f(x) is one-to-one.

h(x) = 2x-4/3

h^-1(x) = 3x+4/2

The formula F(C) = 95 C + 32 calculates the temperature in degrees Fahrenheit, given a temperature in degrees Celsius. You can find an equation for the temperature in degrees Celsius for a given temperature in degrees Fahrenheit by finding the function's

inverse

Check the functions whose inverses are also functions.

second and third

Sample Response: His work is not correct. You first must switch x and y and then solve for y. Compare your response to the sample response above. What did your explanation include?

the conclusion that the work was incorrect an explanation that Talib did not switch the variables at the start an explanation that Talib did not solve for the variable y

If the graph of an inverse passes the __________, you know that the inverse is a function.

vertical-line test

In general, f−1(f(x)) = f(f−1(x)) =

x

The composition of a function and its inverse is always __________.

x

Adjust m and b to graph the equations below. The inverse of y = 2x + 2 is __________.

y = 1/2x - 1

The graph of an inverse is the reflection of the graph of the function over the line __________.

y = x

Is f(x) one-to-one?

yes

The range of the inverse of f(x) is __________.

{-4,-2,0,2,4}

f(x) has domain __________ , and range __________.

{-4,-2,0,2,4} {-2,-1,0,1,2}