# How do you find the domain and range of sqrt(x-1)?

Aug 2, 2018

Domain: $\left[1 , + \infty\right)$
Range: $\left[0 , + \infty\right)$

#### Explanation:

$f \left(x\right) = \sqrt{x - 1}$ :
The square roots are only defined when the expression under the square root is non-negative.

Domain:
$x - 1 \ge 0$
$x \ge 1$

Range:
$\sqrt{x - 1} \ge 0$
$f \left(x\right) \ge 0$