Chapter 5.3, Problem 93AYU

(a)

To determine

To find : The value of $g\left(-1\right)$ and the point on the graph of $g$ .

Explanation of Solution

Given: The equation is $g\left(x\right)=4^x+2$

The value of $g\left(-1\right)$ is calculated as,

  $\begin{array}{c}g\left(-1\right)=4^{-1}+2\\ =\frac{1}{4}+2\\ =\frac{1+8}{4}\\ =\frac{9}{4}\end{array}$

The point on the graph is $\left(-1,\frac{9}{4}\right)$ .

Therefore, the value of $g\left(-1\right)$ is $\frac{9}{4}$ and the point on the graph is $\left(-1,\frac{9}{4}\right)$ .

(b)

To determine

To find : The value of $x$ and the point on the graph of $f$ .

Explanation of Solution

Given: The equation is $g\left(x\right)=4^x+2$ and $g\left(x\right)=66$ .

Equate both the equation of $g\left(x\right)$ to solve for $x$ .

  $\begin{array}{c}{4}^x+2=66\\ 4^x=64\\ 4^x=4^3\\ x=3\end{array}$

The point on the graph is $\left(3,66\right)$ .

Therefore, the value of $x$ is $3$ and the point on the graph is $\left(3,66\right)$ .