How do you find domain and range for g(x)=3/x?

Sep 28, 2015

Domain: $\mathbb{R} - \left\{0\right\}$
Range: $\mathbb{R} - \left\{0\right\}$

Explanation:

Given $g \left(x\right) = \frac{3}{x}$

$g \left(x\right)$ will be defined for all values of $x$ except $x = 0$
Therefore the domain is all Real values except $0$
There are several ways of expressing this; the Answer (above) shows one way; another is $x \in \left(- \infty , 0\right) \cup \left(0 , + \infty\right)$

For the range
$\textcolor{w h i t e}{\text{XXX")g(x) = 3/xcolor(white)("XX")rarrcolor(white)("XX}} x = \frac{3}{g} \left(x\right)$
which is defined for all values of $g \left(x\right) \ne 0$
Therefore the range is also all Real values except $0$.