Chapter 6.3, Problem 3CYU

To determine

The domain and range of the function $f\left(x\right)=\sqrt{x+8}-2$ .

Answer to Problem 3CYU

The domain of the function is $\left\{x|x\ge -8\right\}$ and range of the function is $\left\{y|y\ge -2\right\}$ .

Explanation of Solution

Given information: The given function is,

  $f\left(x\right)=\sqrt{x+8}-\mathrm{2......}\left(1\right)$

Calculation: The domain of the function is defined for which,

  $\begin{array}{c}x+8\ge 0\\ x\ge -8\end{array}$

Hence the domain of the function is $\left\{x|x\ge -8\right\}$ .

And range of the function can be evaluated by substituting the lower limit of domain in the function for which the function is defined. Therefore from (1),

  $\begin{array}{c}f\left(-8\right)=\sqrt{\left(-8\right)+8}-\mathrm{2......}\left(\text{For }x=-8\right)\\ =-2\end{array}$

Hence the range of the function is $\left\{y|y\ge -2\right\}$