Q 59. - Precalculus Enhanced with Graphing Utilities

Question

Graph each function and its inverse on the same Cartesian plane. 

$f\left(x\right)=3^x and f^{-1}\left(x\right)={\log }_{3}x$

Step-by-Step Solution

Answer

The graph is as follows :

Step 1. Given information

Given expressions are :

$$\begin{gathered} f\left(x\right)=3^x \\ {f}^{-1}\left(x\right)={\log }_{3}x \end{gathered}$$

Step 2. Points of the Curve

Points of the function $f\left(x\right)=3^x$

$x$	$f\left(x\right)=3^x$
$1$	$3$
$0$	$1$
$-1$	$0.33$

Step 3. Points of the Curve

Points of the function $f^{-1}\left(x\right)={\log }_{3}x$

$x$	$f^{-1}\left(x\right)={\log }_{3}x$
$3$	$1$
$1$	$0$
$0.33$	$-1$

Step 4. Graph of the given function

The graph of the functions $f\left(x\right)=3^x$ and $f^{-1}\left(x\right)={\log }_{3}x$ is as follows :