Chapter 6.3, Problem 13PPS

To determine

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

Answer to Problem 13PPS

The domain of the function is $\left\{x|x\ge 0\right\}$ and range of the function is $\left\{y|y\le 2\right\}$ .

Explanation of Solution

Given information: The given function is,

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

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

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

Hence the domain of the function is $\left\{x|x\ge 0\right\}$ .

As square-root function is subtracted from a constant number, therefore the upper limit of range can be evaluated by substituting the lower limit of domain in the function for which the function is defined. Therefore from (1),

  $\begin{array}{c}f\left(0\right)=-\sqrt{2\left(0\right)}+\mathrm{2......}\left(\text{For }x=0\right)\\ =2\end{array}$

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