How do you find the range of  f(x)=1/(x-3)?

Jun 18, 2018

$\left(- \infty , 0\right) \cup \left(0 , \infty\right)$

Explanation:

$\text{let } y = \frac{1}{x - 3}$

$\text{rearrange making "x" the subject}$

$y \left(x - 3\right) = 1$

$x y - 3 y = 1$

$x = \frac{1 + 3 y}{y}$

$\text{the denominator } \ne 0$

$\text{range } y \in \left(- \infty , 0\right) \cup \left(0 , \infty\right)$
graph{1/(x-3) [-10, 10, -5, 5]}