# Math Help - Composition & Functoins

1. ## Composition & Functoins

hey all, need help with a problem

Question: Use composition to show that f(x) = (x + 3) / (x - 2) and g(x) = (2x - 3) / (x - 1) are inverse of each other.

Any help would be greatly appreciated, thanks

-Laconian

2. What means that f and g are inverse of each other?
Just that $\forall x \in Dom(g), f(g(x))=x$ and $\forall x \in Dom(f), g(f(x))=x$

For example, let $x \in \mathbb{R}-\{1\},$

$f(g(x))$
$=f(\frac{2x-3}{x-1})$
$=\frac{\frac{2x-3}{x-1}+3}{\frac{2x-3}{x-1}-2}$
$=\frac{2x-3+3(x-1)}{2x-3-2(x-1)}$
$=\frac{5x-6}{-1}$ !!! that's not what we wanted!

But if we change $f(x)=\frac{x+3}{x-1}$ by $f(x)=\frac{x-3}{x-1}$, as you can see, that would work. Then try with $gof$.