Review 6.2 Inverse Functions

Review 6.2 Inverse Functions

By Bette Horsington Algebra 2 at VVA 2022

Multiple Choice

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

• f ^-1(x)
• f ²(x)
• f '(x)
• f ⁺(x)

Multiple Select

$$g\left(x\right)=-7x^5+7$$  Find the inverse of the function.

• $$g^{-1}\left(x\right)=^5\sqrt{\frac{x-7}{7}}$$  

• $$g^{-1}\left(x\right)=-^5\sqrt{\frac{x-7}{7}}$$  

• $$g^{-1}\left(x\right)=^5\sqrt{-\frac{x-7}{7}}$$  

• $$g^{-1}\left(x\right)=-^5\sqrt{\frac{x-7}{7}}$$  

Multiple Choice

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

• $$\frac{x-5}{1}$$  

• $$\frac{x}{5}-1$$  

• $$x-\frac{1}{5}$$  

• $$\frac{x-1}{5}$$  

Multiple Choice

$$f\left(x\right)=\frac{x-2}{6}$$   Find  $$f^{-1}\left(x\right)$$  

• $$\frac{x-6}{2}$$  

• $$6x+2$$  

• $$2x+6$$  

• $$6\left(x+2\right)$$  

Multiple Choice

$$f\left(n\right)=-n^3+2$$   Find the inverse of the function. 

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

• $$f^{-1}\left(n\right)=^3\sqrt{-n+2}$$  

• $$f^{-1}\left(n\right)=2n^5$$  

• $$f^{-1}\left(n\right)=\left(n+3\right)^5$$  

a function and its inverse are reflected over the line

y = x​

​

note how the points are inverted.

​Graphically

​

Multiple Choice

The inverse has been reflected over which line?

• y = x
• x = 0
• y = 0
• x = -y

Multiple Choice

Are these the graphs of two inverse functions?

• Yes
• No
• No way to tell

Multiple Choice

Are these functions inverses?

• No

• Yes

Multiple Choice

Which graph shows inverse functions?

Multiple Choice

Are the pictured functions inverses of each other?

• True
• False

Multiple Choice

f(x) = 3x + 10

g(x) = ⅓x - 3

Find g(f(x))

• f(g(x)) = 1

• f(g(x)) = x

• f(g(x)) = 0

• None of these.

Multiple Choice

Are $$h\left(x\right)=\frac{10+6x}{5}$$   and $$f\left(x\right)=-2x+5$$   inverse functions?

• Inverse Functions

• Not Inverse Functions

Poll

How are you feeling about Inverse Functions?

• Great, this is easy and I ready for quiz.

• Okay, I think I get it, will review a little then take Quiz

• Confused, I am going to ask questions and then take the quiz

• Huh? What's an inverse function?