# How do you find the domain and range of p(x) = sqrt{3/(x - 2)}?

Nov 4, 2017

Domain is $x > 2$ and range is $\left(0 , \infty\right)$

#### Explanation:

In the given function $p \left(x\right) = \sqrt{\frac{3}{x - 2}}$, you cannot have a negative number in the square root. Further, you cannot have $x - 2 = 0$.

Hence domain is $x > 2$.

When $x > 2$as $x \to \infty$, $p \left(x\right) \to 0$ and as $x \to 2$, $p \left(x\right) \to \infty$,

hence range is $\left(0 , \infty\right)$

The graph of $p \left(x\right)$ appears as follows:

graph{sqrt(3/(x-2)) [-6.54, 13.46, -2.44, 7.56]}