# Math Help - Recursive function

1. ## Recursive function

I'm unsure where to post this, so sorry if it's in the wrong place.

How can I find an equation for the following function?

$f(x)=f(x-1)*(g \circ f(x-1))^n -m(h \circ f(x-1))$

Knowing that $f(0) = 10^4$ and that $g(f(t))$ and $r(f(t))$ are linear functions in the form $a*f(t) + b$.

I've tried taking $f(0)$ to evaluate $f(1)$ and then $f(2)$, $f(3)$, etc, to try to see a pattern for $f(x)$, but the only thing I've got so far was:

$f(x)=10^4*\prod_{i=0}^{x-1} (g \circ f(i)^n)-m\sum_{j=0}^{x-2}(r\circ f(j)*\prod_{k=j+1}^{x-1}[g \circ f(k)^n])-m(r\circ f(x-1))$

Which is not a desired expression for the function.

Thanks.