# Math Help - Composition of Functions

1. ## Composition of Functions

f(x) = $1 / (x^3+5)$
g(x) = cubed root of $[(1-5x) / x]$
Find f(g(x))

I understand how to set it up but I keep getting stuck on the algebra.

2. Hi there, I get...

$f(g(x)) = \frac{1}{\left(\sqrt[3]{\frac{1-5x}{x}}\right)^3+5}$

$f(g(x)) = \frac{1}{\frac{1-5x}{x}+5}$

$f(g(x)) = \frac{1}{\frac{1}{x}- \frac{5x}{x}+5}$

$f(g(x)) = \frac{1}{\frac{1}{x}- 5+5}$

$f(g(x)) = \frac{1}{\frac{1}{x}}$

$f(g(x)) = x$

which means $g(x)$ is the inverse of $f(x)$ ??

3. Thanks a lot for your help