# How do you find the domain and range of f(x) = (x - 3)^(1/2)?

Jul 27, 2015

${\left(x - 3\right)}^{\frac{1}{2}}$ is the same as $\sqrt{x - 3}$

#### Explanation:

For square roots the argument must be non-negative, or:
$x - 3 \ge 0 \to x \ge 3$. There is no upper limit.
So the domain is $3 \le x < \infty$

When $x = 3 \to f \left(x\right) = 0$, in other words $f \left(x\right) \ge 0$
Also here there is no upper limit as $x$ gets larger.
So the range is $0 \le f \left(x\right) < \infty$
graph{sqrt(x-3) [-6.56, 25.48, -4.6, 11.43]}