# How do you find f(g(x)) if g(x) = 3/(x - 1) and f(x) = (x - 1)/(x - 3)?

Feb 1, 2017

The answer is $= \frac{4 - x}{6 - 3 x}$

#### Explanation:

This is a composition of functions

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

$g \left(x\right) = \frac{3}{x - 1}$

$f \left(g \left(x\right)\right) = f \left(\frac{3}{x - 1}\right)$

$= \frac{\left(\frac{3}{x - 1}\right) - 1}{\left(\frac{3}{x - 1}\right) - 3}$

$= \frac{3 - \left(x - 1\right)}{3 - 3 \left(x - 1\right)}$

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

$= \frac{4 - x}{6 - 3 x}$