Finding Inverses of Functions

What does it mean to find the inverse of a function?

• the x's and y's are switched
• the x's and y's are divided by 2
• the x's and y's are made negative
• the x's and y's are the same

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.4

Find the inverse of  $f\left(x\right)=12x-3$  

•  $f^{-1}\left(x\right)=\frac{x+3}{12}$  

•  $f^{-1}\left(x\right)=\frac{x-3}{12}$  

•  $f^{-1}\left(x\right)=\frac{x+12}{3}$  

•  $f^{-1}\left(x\right)=\frac{x-12}{3}$  

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.4

CCSS.HSF.IF.C.8

Find the inverse of  $f\left(x\right)=-\frac{5}{8}x+10$  

•  $f^{-1}\left(x\right)=-\frac{8}{5}x-10$  

•  $f^{-1}\left(x\right)=10\left(x-\frac{8}{5}\right)$  

•  $f^{-1}\left(x\right)=-\frac{5}{8}\left(x-10\right)$  

•  $f^{-1}\left(x\right)=-\frac{8}{5}\left(x-10\right)$  

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.4

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.HSA.REI.B.4

CCSS.HSF.BF.B.4

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.HSA.REI.B.4

CCSS.HSF.BF.B.4