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?

Short 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$(-2,\frac{1}{9})$.

Step-by-step solution

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

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)=19.

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 $(-2,\frac{1}{9})$.