Q. 93 - Precalculus Enhanced with Graphing Utilities

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?

Step-by-Step Solution

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 $(3,66)$.

Part (a) Step 1. Substitute x = - 1 in g ( x ) = 4 x + 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 $(3,66)$.