Chapter 4.6, Problem 3QR

Solution

To determine : The domain and range of the function $f\left(x\right)=\sqrt{x-1}$ .

The domain of the given function is $\left(-\infty ,\infty \right)$ and its range is $\left[-2,2\right]$ .

Given information :

The function $f\left(x\right)=\sqrt{x-1}$ .

Concept used:

The domain of a function is the set of all the real values for which the function is meaningful and range of a function is the set of all real values taken by the function at points in its domain.

Explanation :

Consider the given function $f\left(x\right)=\sqrt{x-1}$ .

Here, $f\left(x\right)$ is meaningful for all the values if $x-1>0$ . That implies $x>1$ and it assumes all real values greater than or equal to zero.

Therefore, the domain of the given function is $\left(1,\infty \right)$ and its range is $\left[0,\infty \right)$ .