# What is the domain and range of f(x) = (3 - x)^(1/2)?

May 5, 2017

Domain : $x \le 3 \mathmr{and} \left(- \infty , 3\right]$
Range : $f \left(x\right) \ge 0 \mathmr{and} \left[0 , \infty\right)$
$f \left(x\right) = \sqrt{3 - x}$. for domain, under root should not be less than $0 \therefore \left(3 - x\right) \ge 0 \mathmr{and} x \le 3$ or Domain : $\left(- \infty , 3\right]$
Range is $f \left(x\right) \ge 0$ or Range : $\left[0 , \infty\right)$ graph{(3-x)^0.5 [-14.24, 14.23, -7.12, 7.12]} [Ans]