Module 1: Inverse Functions

Find the inverse of the following function.

 $f\left(x\right)\ =\ x$  

•  $f^{-1}\left(x\right)\ =\ 2x$  

•  $f^{-1}\left(x\right)\ =\ x$  

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

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

Find the inverse of the following function.

 $f\left(x\right)\ =\ \frac{x+5}{2}$  

•  $f^{-1}\left(x\right)\ =\ 2x-5$  

•  $f^{-1}\left(x\right)\ =\ 5x-2$  

•  $f^{-1}\left(x\right)\ =\ 2x+5$  

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

Find the inverse of the following function.

 $f\left(x\right)\ =\ 7x-3$  

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

•  $f^{-1}\left(x\right)\ =\ 3x+7$  

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

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

Find the inverse of the following function.

 $f\left(x\right)\ =\ x^2+4$  

•  $f^{-1}\left(x\right)\ =\ x^4-2$  

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

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

•  $f^{-1}\left(x\right)=x^2-4$  

Find the inverse of the following function.

 $f\left(x\right)\ =\ 5x^2$  

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

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

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

•  $f^{-1}\left(x\right)=\sqrt{2x^5}$  

Find the inverse of the following function.

 $f\left(x\right)\ =\ 2^x$  

•  $f^{-1}\left(x\right)\ =\ \log_2x$  

•  $f^{-1}\left(x\right)\ =\ \log_x2$  

•  $f^{-1}\left(x\right)\ =\ -2^x$  

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

Find the inverse of the following function.

 $f\left(x\right)\ =\ 4^x+1$  

•  $f^{-1}\left(x\right)\ =\ \log_4\left(x\right)-1$  

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

•  $f^{-1}\left(x\right)\ =\ \log_4\left(x-1\right)$  

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

Find the inverse of the following function.

 $f\left(x\right)\ =\ \log_7x$  

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

•  $f^{-1}\left(x\right)\ =\ \frac{1}{\log_7x}$  

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

•  $f^{-1}\left(x\right)=7^x$  

Find the inverse of the following function.

 $f\left(x\right)\ =\ \log_5\left(x+2\right)$  

•  $f^{-1}\left(x\right)\ =\ \log_2\left(x+5\right)$  

•  $f^{-1}\left(x\right)\ =\ \frac{1}{\log_5\left(x-2\right)}$  

•  $f^{-1}\left(x\right)\ =\ 5^x-2$  

•  $f^{-1}\left(x\right)=2^x-5$  

Find the inverse of the following function.

 $f\left(x\right)\ =\ x^{\Delta}+5$  

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

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

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

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