Q. 92 - Precalculus Enhanced with Graphing Utilities

Question

Suppose that $f\left(x\right)=3^x$.

(a) What is $f\left(4\right)$? What point is on the graph of f?

(b) If $f\left(x\right)=\frac{1}{9}$, what is x? What point is on the graph of f?

Step-by-Step Solution

Answer

Part (a) $f\left(4\right)=81$ and the point on graph is $(4,81)$.

Part (b) $x=-2$ and the point on the graph is $(-2,\frac{1}{9})$.

Part (a) Step 1. Substitute x = 4 in f ( x ) = 3 x .

This gives

$$\begin{gathered} f\left(4\right)=3^4 \\ f\left(4\right)=81 \end{gathered}$$

The point on the graph of the function f is $(4,81)$.

Part (b) Step 1. Finding value of x using f ( x ) = 1 9 .

This gives

$$\begin{gathered} f\left(x\right)=\frac{1}{9} \\ {3}^x=\frac{1}{9} \\ {3}^x=9^{-1} \\ {3}^x={\left(3^2\right)}^{-1} \\ 3^x=3^{-2} \end{gathered}$$

On comparing

$x=-2$

The point on the graph of the function f is $(-2,\frac{1}{9})$.