Q 62. - Precalculus Enhanced with Graphing Utilities

Question

Graph each function and its inverse on the same Cartesian plane 

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

Step-by-Step Solution

Answer

The graph of the given expression is 

Step 1. Given information

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

Step 2. Points of the Curve

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

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

Step 3. Points of the Curve

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

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

Step 4. Graph of the functions

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