Chapter 7.6, Problem 40PPS

To determine

By using the graph of the given function $f\left(x\right)={\left(\frac{1}{2}\right)}^x$ write the value of $n$ for its given equation of $g\left(x\right)$ .

Answer to Problem 40PPS

The value of $n$ is $n=\frac{1}{0.7}$

So, the equation of $g\left(x\right)=f\left(nx\right)$ becomes $g\left(x\right)=f\left(\frac{1}{0.7}x\right)$

Explanation of Solution

Given information:

It is given in the question that, the parent function is $f\left(x\right)={\left(\frac{1}{2}\right)}^x$

And the graph of given function $g\left(x\right)=f\left(nx\right)$ is,

  

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

  

By observing the graph of the two given functions, the graph of $g\left(x\right)=f\left(nx\right)$ is horizontal compress with the $factor-\frac{1}{0.7}$ which is only possible when the value of $n$ is $n=\frac{1}{0.7}$

So, the equation of $g\left(x\right)=f\left(nx\right)$ becomes $g\left(x\right)=f\left(\frac{1}{0.7}x\right)$