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

Aug 11, 2017

Domain : $x \le 1 \mathmr{and} \left(- \infty .1\right]$
Range : f(x) >=0 or [0 ,oo)#

#### Explanation:

$f \left(x\right) = \sqrt{1 - x}$ . Domain: Under root should not be negative

quantity. So Domain : $1 - x \ge 0 \mathmr{and} 1 \ge x \mathmr{and} x \le 1$

Domain is $x \le 1 \mathmr{and} \left(- \infty .1\right]$

Range : Minimum value of $f \left(x\right) = 0$ when $x = 1$ and maximum

value is limitless $\infty$. So range : $f \left(x\right) \ge 0 \mathmr{and} \left[0 , \infty\right)$

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