Chapter EP, Problem 9.3.7EP

To determine

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

Answer to Problem 9.3.7EP

Domain and range of the function $f\left(x\right)=\frac{7}{x+10}$ are $ℝ-\left\{-10\right\}$ and $ℝ$ respectively

Explanation of Solution

Given: $f\left(x\right)=\frac{7}{x+10}$

The given $f\left(x\right)=\frac{7}{x+10}$ and graph of the function $f\left(x\right)=\frac{7}{x+10}$ is

Now it has to state domain and range of the given function $f\left(x\right)=\frac{7}{x+10}$

Domain of the function $f\left(x\right)=\frac{7}{x+10}$ is $ℝ-\left\{-10\right\}$ .

  $\begin{array}{l}f\left(x\right)=\frac{7}{x+10}\\ f\left(-10\right)=\frac{7}{-10+10}\\ =\frac{7}{0}\\ =\infty \end{array}$

Range of the function $f\left(x\right)=\frac{7}{x+10}$ is $ℝ$ .

Hence, domain and range of the function $f\left(x\right)=\frac{7}{x+10}$ are $ℝ-\left\{-10\right\}$ and $ℝ$ respectively.