Section 6.7: Inverse Function

Find the inverse of

 $f\left(x\right)=-4x-12$  

•  $f^{-1}\left(x\right)=4x-3$  

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

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

•  $f^{-1}\left(x\right)=-4x-3$  

Find the inverse of

 $f\left(x\right)=\frac{1}{4}x-7$  

•  $f^{-1}\left(x\right)=4x+7$  

•  $f^{-1}\left(x\right)=-4x+28$  

•  $f^{-1}\left(x\right)=-4x-7$  

•  $f^{-1}\left(x\right)=4x+28$  

Find the inverse of

 $f\left(x\right)=3x-5$  

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

•  $f^{-1}\left(x\right)=3x+5$  

•  $f^{-1}\left(x\right)=3y-5$  

•  $f^{-1}\left(x\right)=3y+5$  

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

Determine if these are Inverse Functions 

 $f\left(x\right)=\frac{10+6x}{5}$   and  $g\left(x\right)=-2x+5$  

• Yes, they are Inverse Functions

• No, they are NOT Inverse Functions

Determine if these are Inverse Functions 

 $f\left(x\right)=4+\frac{1}{3}x$   and  $g\left(x\right)=3x-12$  

• Yes, they are Inverse Functions

• No, they are NOT Inverse Functions

Determine if these are Inverse Functions 

 $f\left(x\right)=-7x-4$   and  $g\left(x\right)=\frac{-x-4}{7}$  

• Yes, they are Inverse Functions

• No, they are NOT Inverse Functions

Find the inverse of

 $f\left(x\right)=\frac{-9-7x}{3}$  

•  $f^{-1}\left(x\right)=\frac{-3x-9}{7}$  

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

•  $f^{-1}\left(x\right)=\frac{5}{8}x-\frac{17}{8}$  

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

If the equation of  $f\left(x\right)$  goes through the points $\left(1,4\right)$  and  $\left(4,6\right)$  , what points does  $f^{-1}\left(x\right)$   go through?

•  $\left(1,4\right)$  and  $\left(4,6\right)$  

•  $\left(-4,-1\right)$  and  $\left(-6,-4\right)$  

•  $\left(-1,-4\right)$  and  $\left(-4,-6\right)$  

•  $\left(4,1\right)$  and  $\left(6,4\right)$  

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

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

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

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

•  $f^{-1}\left(x\right)=x^2-5$