Question

Suppose that $g\left(x\right)=4^x+2$.

(a) What is $g(-1)$? What point is on the graph of g?

(b) If $g\left(x\right)=66$, what is x? What point is on the graph of g?

Short answer

Part (a) $g(-1)=\frac{9}{4}$and the point on the graph of g is $(-1,\frac{9}{4})$.

Part (b)$x=3$and the point on the graph of g is$(3,66)$.

Step-by-step solution

Part (a) Step 1. Substitute x=-1 in g(x)=4x+2.

This gives

$$\begin{gathered} g(-1)=4^{-1}+2 \\ g(-1)=\frac{1}{4}+2 \\ g(-1)=\frac{9}{4} \end{gathered}$$

The point on the graph of the function g is$(-1,\frac{9}{4})$.

Part (b) Step 1. Finding value of x using f(x)=66.

This gives

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

On comparing

$x=3$

The point on the graph of the function g is$(3,66)$.