Horizontal Line Test

Use the horizontal line test to determine if the function has an inverse function.

• yes

• no

Use the horizontal line test to determine if the function has an inverse function.

• yes

• no

Use the horizontal line test to determine if the function has an inverse function.

• yes

• no

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.IF.A.1

Use the horizontal line test to determine if the function has an inverse function.

• yes

• no

Determine if the function has an inverse function. If it does, then find the inverse function.

 $f\left(x\right)=x^4$  

• yes,  $f^{-1}\left(x\right)=4x$  

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

• yes,  $f^{-1}\left(x\right)=x+4$  

• no inverse

Determine if the function has an inverse function. If it does, then find the inverse function.

 $f\left(x\right)=\frac{x}{8}$  

• yes,  $f^{-1}\left(x\right)=8x$  

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

• yes,  $f^{-1}\left(x\right)=x+8$  

• no inverse

Determine if the function has an inverse function. If it does, then find the inverse function.

 $f\left(x\right)=\sqrt{2x+3}$  

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

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

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

• no inverse

Tags

CCSS.HSF-BF.B.4D

Determine if the function has an inverse function. If it does, then find the inverse function.

 $f\left(x\right)=-\frac{4}{x^2}$  

• yes,  $f^{-1}\left(x\right)=4x^2$  

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

• yes,  $f^{-1}\left(x\right)=2x-4$  

• no inverse

Determine if the function has an inverse function. If it does, then find the inverse function.

 $f\left(x\right)=2x+8$  

• yes,  $f^{-1}\left(x\right)=8x-2$  

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

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

• no inverse

Determine if the function has an inverse function. If it does, then find the inverse function.

 $f\left(x\right)=\left(x-5\right)^2$  

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

• yes,  $f^{-1}\left(x\right)=\ x^2-10x+25$  

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

• no inverse