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

Jul 9, 2015

Assuming the domain is $\mathbb{R}$ \ $\left\{0\right\}$, then the range is $\left(0 , \infty\right)$.

#### Explanation:

If $x \in \mathbb{R}$ then ${x}^{2} \ge 0$ and $\frac{3}{x} ^ 2 > 0$ except when $x = 0$..

If $x = 0$ then ${x}^{2} = 0$ and $\frac{3}{{x}^{2}} = \frac{3}{0}$ is undefined.

For any $y \in \left(0 , \infty\right)$ if $x = \sqrt{\frac{3}{y}}$ then $f \left(x\right) = \frac{3}{\sqrt{\frac{3}{y}}} ^ 2 = \frac{3}{\frac{3}{y}} = y$.

So the range of $f \left(x\right)$ is the whole of $\left(0 , \infty\right)$