Q. 91 - Precalculus Enhanced with Graphing Utilities

Question

Suppose that $f\left(x\right)=2^x$.

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

(b) If $f\left(x\right)=\frac{1}{16}$, what is x? What point is on the graph of f?

Step-by-Step Solution

Answer

Part (a) $f\left(4\right)=16$ and the point on the graph is $(4,16)$.

Part (b) $x=-4$ and the point on the graph is $(-4,\frac{1}{16})$.

Part (a) Step 1. Substitute x = 4 in f ( x ) = 2 x .

This gives

$$\begin{gathered} f\left(4\right)=2^4 \\ f\left(4\right)=16 \end{gathered}$$

So the point on the graph of the function f is $(4,16)$.

Part (b) Step 1. Find value of x using f ( x ) = 1 16 .

$$\begin{gathered} f\left(x\right)=\frac{1}{16} \\ {2}^x=\frac{1}{16} \\ {2}^x={16}^{-1} \\ {2}^x={\left(2^4\right)}^{-1} \\ 2^x=2^{-4} \end{gathered}$$

On comparing,

$x=-4$

So the point on the graph is $(-4,\frac{1}{16})$