# How do you find the domain and range of g(x) = sqrt(x-4) ?

Mar 30, 2018

Domain : $x \ge 4 \mathmr{and} \left[4 , \infty\right)$
Range : $g \left(x\right) \ge 0 \mathmr{and} \left[0 , \infty\right)$

#### Explanation:

g(x)=sqrt(x-4); g(x) is undefined at $x < 4 \therefore x \ge 4$

Hence domain is $x \ge 4 \mathmr{and} \left[4 , \infty\right)$

Range: Output of square root is $\ge 0 \therefore g \left(x\right) \ge 0$

Hence range is $g \left(x\right) \ge 0 \mathmr{and} \left[0 , \infty\right)$

graph{(x-4)^0.5 [-20, 20, -10, 10]} [Ans]