# How do you find the domain and range of f(x) = sqrt(x-4) +6?

Jan 26, 2017

The domain is x in [4, +oo[
The range is f(x) in [6,+oo[

#### Explanation:

What is under the sqrt sign is $\ge 0$

$x - 4 \ge 0$

$x \ge 4$

The domain of $f \left(x\right)$ is D_f(x)= [4, +oo[

When $x = 4$, $f \left(4\right) = 6$

${\lim}_{x \to + o} f \left(x\right) = + \infty$

The range is R_f(x)=[6,+oo[