Q. 94 - Precalculus Enhanced with Graphing Utilities

Question

Suppose that $g\left(x\right)=5^x-3$.

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

(b) If $g\left(x\right)=122$, what is x? What point is on the graph of g?

Step-by-Step Solution

Answer

Part (a) $g(-1)=-\frac{14}{5}$ and the point on the graph of g is $-1,-\frac{14}{5}$.

Part (b) $x=3$ and the point on the graph of g is $(3,122)$.

Part (a) Step 1. Substitute x = - 1 in g ( x ) = 5 x - 3 .

This gives

$$\begin{gathered} g(-1)=5^{-1}-3 \\ =\frac{1}{5}-3 \\ =-\frac{14}{5} \end{gathered}$$

The point on the graph of the function g is $(-1,-\frac{14}{5})$.

Part (b) Step 1. Finding x using g ( x ) = 122 .

We have

$$\begin{gathered} g\left(x\right)=122 \\ {5}^x-3=122 \\ {5}^x=122+3 \\ {5}^x=125 \\ {5}^x=5^3 \end{gathered}$$

On comparing,

$x=3$

The point on the graph of the function g is $(3,122)$.