Inverse Functions

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

• f ^-1(x)
• f ²(x)
• f '(x)
• f ⁺(x)

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

• $f^{-1}(x)=\frac{3}{5}+x$

• $f^{-1}(x)=3x+5$

• $f^{-1}(x)=5x+3$

The inverse of $f(x)=x+30$   is   $f^{-1}(x)=x-30$  .

• True

• False

• I have no idea how to do this.

The inverse of $f(x)=8x+30$  is  $f^{-1}(x)=\frac{8}{30}$  .

• True

• False

 $f\left(x\right)=x+5.\ Find\ the\ \exp ression\ of\ f^{-1}\left(x\right)$  

•  $f^{-1}\left(x\right)=x+5$  

•  $f^{-1}\left(x\right)=x-5$  

•  $f^{-1}\left(x\right)=5-x$  

• none of the above

 $f\left(x\right)\ =\ \frac{x}{3}.\ Find\ the\ \exp ression\ of\ f^{-1}\left(x\right).$  

•  $f^{-1}\left(x\right)=3x$  

•  $f^{-1}\left(x\right)=3y$  

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

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

 $g\left(x\right)=\sqrt{x}.\ Find\ \exp ression\ of\ g^{-1}\left(x\right).$  

•  $g^{-1}\left(x\right)=\ 2x$  

•  $g^{-1}\left(x\right)=\ y^2$  

•  $g^{-1}\left(x\right)=\ x^2$  

• none of the above

 $f\left(x\right)=\left(x-7\right)^2.\ Find\ \exp ression\ of\ f^{-1}\left(x\right).$  

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

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

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

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

 $g\left(x\right)=\ \frac{2}{x+1}.\ Find\ the\ \exp ression\ of\ g^{-1}\left(x\right).$  

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

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

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

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

Choose two answers.

g(x) = 2x + 5.
(a) Find g-1(x)
(b) Evaluate g-1(-3)

•  $\left(a\right)g^{-1}\left(x\right)=\frac{x-5}{2}$  

•  $\left(a\right)g^{-1}\left(x\right)=\frac{x}{2}-5$  

•  $\left(b\right)g^{-1}\left(-3\right)=-4$  

•  $\left(b\right)g^{-1}\left(-3\right)=4$