# How do you find the inverse of f(x)= (2x+1)/(x-3)?

Jan 10, 2016

${f}^{-} 1 \left(x\right) = \frac{1 + 3 x}{x - 2}$

#### Explanation:

An inverse graph is found by reflecting the original graph in the line y=x. The easiest way to find the inverse function is by setting y=f(x), making x the subject and then switching y and x.

$y = \frac{2 x + 1}{x - 3}$

$y \left(x - 3\right) = 2 x + 1$

$x y - 3 y = 2 x + 1$

$x y - 2 x = 1 + 3 y$

$x \left(y - 2\right) = 1 + 3 y$

$x = \frac{1 + 3 y}{y - 2}$

Therefore ${f}^{-} 1 \left(x\right) = \frac{1 + 3 x}{x - 2}$