Inverse of a Function Graphs

​1.8 Inverse Functions

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Multiple Choice

The inverse of the function f(x) is written as ...#1

• f ^-1(x)
• f ²(x)
• f '(x)
• f ⁺(x)

Multiple Choice

The inverse has been reflected over which line? #2

• y = x
• x = 0
• y = 0
• x = -y

Multiple Choice

State if the given functions are inverses. #5

• yes

• no

Multiple Choice

Find the inverse of f(x) = -4x - 12. #6

• f^-1(x) = 4x - 3
• f^-1(x) = -1/4x - 3
• f^-1(x) = 1/4x + 3
• f^-1(x) = -4x - 3

Multiple Choice

Was the inverse function found correctly? #11

• no

• yes

Multiple Choice

When finding the inverse of a relation,  1st you replace f(x) with y, and 2nd you switch the x's and y's. What do you do next? #13

• solve for y
• replace y with f^-1(x)
• solve for x
• find the greatest common factor

Multiple Choice

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through? #14

• (1, 4) and (4, 6)
• (-4, -1) and (-6, -4)
• (-1, -4) and (-4, -6)
• (4, 1) and (6, 4)

Multiple Select

Which pairs of the following functions are inverses? #15

Multiple Choice

Find the inverse of the function including any restriction on the domain. #16

• f^-1 = x³ − 5, x ≥ 5
• f^-1 = x³ + 5,  x ≥ 0
• f^-1 = x³ + 5
• Inverse does not exist

Multiple Choice

Find the inverse of

$$f\left(x\right)\ =\ \sqrt{x-5}$$  . #21

• $$f^{-1}\left(x\right)\ =\ x^2-\ 5$$  

• $$f^{-1}\left(x\right)\ =\ x^2+5$$  

• $$f^{-1}\left(x\right)\ =\ \left(x+5\right)^2$$  

• $$f^{-1}\left(x\right)\ =\ \left(x\ -5\right)^2$$  

Multiple Choice

Which of the following is NOT TRUE about inverse functions? #26

• Inverse functions are reflections of each other over the line y = x.

• You find the inverse by switching x and y in the equation.

• The domain of a function always becomes the domain of its inverse.

• The domain of a function always becomes the range of its inverse.

Multiple Choice

A function has an inverse function if... #34

• It passes the Vertical Line Test

• It fails the Horizontal Line Test

• It passes the Horizontal Line Test

• It fails the Vertical Line Test

Multiple Choice

Find the inverse function. #40

Multiple Choice

Which graph represents the functions f(x) and f^-1(x)? #32

Multiple Choice

Which of the following best describes the graph? #29

• They are both functions, but not inverse functions.

• They are reflected over y=x, but they are not both functions.

• They are not reflected over y=x, and they are not both functions.

• They are inverse functions.