Chapter 6.4, Problem 18E

To determine

To find: The function of $f$ represented by $g$ and draw the graph.

Answer to Problem 18E

Both the graph of the function are increases exponentially starting from $-\infty$ and graph of g(x) is shrink by the factor $\frac{4}{3}$ .

Explanation of Solution

Given information:

The given functions are $f\left(x\right)=e^x$ and $g\left(x\right)=\frac{4}{3}{e}^x$ .

Consider thegiven functions are $f\left(x\right)=e^x$ and $g\left(x\right)=\frac{4}{3}{e}^x$ .

Write the function of $f$ in terms of the function $g$

  $\begin{array}{c}g\left(x\right)=\frac{4}{3}{e}^x\\ g\left(x\right)=\frac{4}{3}f\left(x\right)\\ f\left(x\right)=\frac{3}{4}g\left(x\right)\end{array}$

Now, draw the graph.

  

Hence, both the graph of the function are increases exponentially starting from $-\infty$ and graph of g(x) is shrink by the factor $\frac{4}{3}$ .