Chapter 6.3, Problem 5CYU

To determine

The domain and range of the function $f\left(x\right)=3\sqrt{x-1}$ . And sketch the graph of the function.

Answer to Problem 5CYU

The domain of the function is $\left\{x|x\ge 1\right\}$ and range of the function is $\left\{y|y\ge 0\right\}$ .

Explanation of Solution

Given information: The given function is,

  $f\left(x\right)=3\sqrt{x-1}\mathrm{....}\left(1\right)$

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

  $\begin{array}{c}x-1\ge 0\\ x\ge 1\end{array}$

Hence the domain of the function is $\left\{x|x\ge 1\right\}$ .

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),

  $\begin{array}{c}f\left(1\right)=3\sqrt{\left(1\right)-1}\mathrm{......}\left(\text{For }x=1\right)\\ =0\end{array}$

Hence the range of the function is $\left\{y|y\ge 0\right\}$

Graph: The graph for the function is shown as,