Q 61. - Precalculus Enhanced with Graphing Utilities

Question

Graph each function and its inverse on the same Cartesian plane 

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

Step-by-Step Solution

Answer

The graph of the given expressions is :

Step 1. Given information

Given expressions are 

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

Step 2. Points of the Curve

Points of the function $f\left(x\right)={\left(\frac{1}{2}\right)}^x$

$x$	$f\left(x\right)={\left(\frac{1}{2}\right)}^x$
$1$	$0.5$
$0$	$1$
$-1$	$2$

Step 3. Points of the Curve

Points of the function  $f^{-1}\left(x\right)={\log }_{\frac{1}{2}}x$

x	$f^{-1}\left(x\right)={\log }_{\frac{1}{2}}x$
$4$	$-2$
$1$	$0.5$
$0.25$	$2$

Step 4. Graph of the functions

The graph of the functions $f\left(x\right)={\left(\frac{1}{2}\right)}^x$ and $f^{-1}\left(x\right)={\log }_{\frac{1}{2}}x$ is as follows :