Q. 2 - Precalculus Enhanced with Graphing Utilities

Question

Find the domain of each function and evaluate each function at $x=-1$.

$f\left(x\right)=\sqrt{4 - 5x}$

Step-by-Step Solution

Answer

The domain of the function $f\left(x\right)$ is $\left\{x|x\le \frac{4}{5}\right\}$

The value at $x=-1$ is $3$.

Step 1. Find the domain of the function.

$f\left(x\right)=\sqrt{4-5x}$

For domain,

$$\begin{gathered} 4-5x\ge 0 \\ 4\ge 5x \\ x\le \frac{4}{5} \end{gathered}$$

Step 2. Find value of f ( x ) at x = - 1

$$\begin{gathered} f\left(x\right)=\sqrt{4-5x} \\ f(-1)=\sqrt{4-5(-1)} \\ f(-1)=\sqrt{4+5} \\ f(-1)=\sqrt{9} \\ f(-1)=3 \end{gathered}$$