Inverses of Functions

What is the first step in finding the equation of the inverse of a function?

• get x by itself
• switch x and y
• solve for y
• write the function in inverse function notation

Tags

CCSS.HSF-BF.B.4A

Find the inverse of  $f\left(x\right)=3x+2$  

•  $f^{-1}\left(x\right)=\frac{x-2}{3}$  

•  $f^{-1}\left(x\right)=\frac{x-3}{2}$  

•  $f^{-1}\left(x\right)=\frac{3x}{2}$  

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

Tags

CCSS.HSF-BF.B.4A

Find the inverse of  $f\left(x\right)=-5x-7$  

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

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

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

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

Tags

CCSS.HSF-BF.B.4A

Find the inverse of  $f\left(x\right)=-\frac{3}{4}x+5$  

•  $f^{-1}\left(x\right)=5\left(x-\frac{4}{3}\right)$  

•  $f^{-1}\left(x\right)=-\frac{3}{4}\left(x-5\right)$  

•  $f^{-1}\left(x\right)=-\frac{4}{3}\left(x-5\right)$  

•  $f^{-1}\left(x\right)=-5\left(x-\frac{3}{4}\right)$  

Tags

CCSS.HSF-BF.B.4A

Find the inverse of  $f\left(x\right)=\frac{1}{2}x+8$  

•  $f^{-1}\left(x\right)=2x+8$  

•  $f^{-1}\left(x\right)=2x-16$  

•  $f^{-1}\left(x\right)=2\left(x+8\right)$  

•  $f^{-1}\left(x\right)=\frac{1}{2}x-16$  

Tags

CCSS.HSF-BF.B.4A

Find the inverse of  $f\left(x\right)=x^2+5$  

•  $f^{-1}\left(x\right)=x-25$  

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

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

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

Tags

CCSS.HSF-BF.B.4A

Find the inverse of  $f\left(x\right)=x^2-4$  

•  $f^{-1}\left(x\right)=\sqrt{x+16}$  

•  $f^{-1}\left(x\right)=\sqrt{x-4}$  

•  $f^{-1}\left(x\right)=\sqrt{x}+4$  

•  $f^{-1}\left(x\right)=\sqrt{x+4}$  

Tags

CCSS.HSF-BF.B.4A

Find the inverse of $f\left(x\right)=\left(x-6\right)^2$  

•  $f^{-1}\left(x\right)=\sqrt{x}+6$  

•  $f^{-1}\left(x\right)=\sqrt{x+6}$  

•  $f^{-1}\left(x\right)=\sqrt{x}-6$  

•  $f^{-1}\left(x\right)=\sqrt{x-6}$  

Tags

CCSS.HSF-BF.B.4A

When two functions are inverses of each other, their graphs are reflective over...

• y=x

• x-axis

• y-axis

Tags

CCSS.HSF-BF.B.4C

Are these functions inverses?

• No
• Yes
• No way to tell

Tags

CCSS.HSF-BF.B.4B