Chapter EP, Problem 9.3.5EP

To determine

To state: The domain and range of the given function and draw the graph of the function

Answer to Problem 9.3.5EP

Domain and range of the function $f\left(x\right)=\frac{-1}{x-4}$ are $ℝ-\left\{4\right\}$ and $ℝ$ respectively

Explanation of Solution

Given: $f\left(x\right)=\frac{-1}{x-4}$

The given $f\left(x\right)=\frac{-1}{x-4}$ and graph of the function $f\left(x\right)=\frac{-1}{x-4}$ is

Now it has to state domain and range of the given function $f\left(x\right)=\frac{-1}{x-4}$

Domain of the function $f\left(x\right)=\frac{-1}{x-4}$ is $ℝ-\left\{4\right\}$ .

  $\begin{array}{l}f\left(x\right)=\frac{-1}{x-4}\\ f\left(4\right)=\frac{-1}{4-4}\\ =\frac{-1}{0}\\ =\infty \end{array}$

Range of the function $f\left(x\right)=\frac{-1}{x-4}$ is $ℝ$ .

Hence, domain and range of the function

$f\left(x\right)=\frac{-1}{x-4}$ are $ℝ-\left\{4\right\}$ and $ℝ$ respectively.