# How do you find the domain and range of sqrt{1 - x}?

Jul 18, 2018

Domain : $x \le 1 \mathmr{and} x \in \left(- \infty , 1\right]$
Range : $f \left(x\right) \ge 0 \mathmr{and} f \left(x\right) \in \left[0 , \infty\right)$

#### Explanation:

$f \left(x\right) = \sqrt{1 - x}$ , domain is possible input of x ; f(x) is

undefined when $\left(1 - x\right) < 0 \therefore \left(1 - x\right) \ge 0 \mathmr{and} 1 \ge x$

or $x \le 1 \therefore$ Domain : $x \le 1 \mathmr{and} x \in \left(- \infty , 1\right]$

Range is resulting output of $f \left(x\right) \therefore f \left(x\right) \ge 0$

Range : $f \left(x\right) \ge 0 \mathmr{and} f \left(x\right) \in \left[0 , \infty\right)$

graph{sqrt (1-x) [-10, 10, -5, 5]}[Ans]