Chapter 6.3, Problem 15PPS

To determine

The domain and range of the function $f\left(x\right)=4\sqrt{x-2}-8$ .

Answer to Problem 15PPS

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

Explanation of Solution

Given information: The given function is,

  $f\left(x\right)=4\sqrt{x-2}-\mathrm{8......}\left(1\right)$

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

  $\begin{array}{c}x-2\ge 0\\ x\ge 2\end{array}$

Hence the domain of the function is $\left\{x|x\ge 2\right\}$ .

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),

  $\begin{array}{c}f\left(x\right)=4\sqrt{\left(2\right)-2}-\mathrm{8......}\left(\text{For }x=2\right)\\ =-8\end{array}$

Hence the range of the function is $\left\{y|y\ge -8\right\}$