
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?
$\displaystyle f(x)=f(x1)*(g \circ f(x1))^n m(h \circ f(x1))$
Knowing that $\displaystyle f(0) = 10^4$ and that $\displaystyle g(f(t))$ and $\displaystyle r(f(t))$ are linear functions in the form $\displaystyle a*f(t) + b$.
I've tried taking $\displaystyle f(0)$ to evaluate $\displaystyle f(1)$ and then $\displaystyle f(2)$, $\displaystyle f(3)$, etc, to try to see a pattern for $\displaystyle f(x)$, but the only thing I've got so far was:
$\displaystyle f(x)=10^4*\prod_{i=0}^{x1} (g \circ f(i)^n)m\sum_{j=0}^{x2}(r\circ f(j)*\prod_{k=j+1}^{x1}[g \circ f(k)^n])m(r\circ f(x1))$
Which is not a desired expression for the function.
Thanks.