Q 60. - Precalculus Enhanced with Graphing Utilities

Question

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

$$\begin{gathered} f\left(x\right)=4^x \\ {f}^{-1}\left(x\right)={\log }_{4}x \end{gathered}$$

Step-by-Step Solution

Answer

The graph of the given expression is :

Step 1. Given information

Given expressions are $$\begin{gathered} f\left(x\right)=4^x \\ {f}^{-1}\left(x\right)={\log }_{4}x \end{gathered}$$

Step 2. Points of the Curve

Points of the function $f\left(x\right)=4^x$

$x$	$f\left(x\right)=4^x$
$1$	$4$
$0$	$1$
$-1$	$0.25$

Step 3. Points of the Curve

Points of the function $f^{-1}\left(x\right)={\log }_{4}x$

$x$	$f^{-1}\left(x\right)={\log }_{4}x$
$4$	$1$
$1$	$0$
$0.25$	$-1$

Step 4. Graph of the functions

The graph of the functions $f\left(x\right)=4^x$and $f^{-1}\left(x\right)={\log }_{4}x$ is as follows :