PRMO level question of functions Consider the functions $f(x)$ and $g(x)$ which are defined as $f(x)=(x+1)(x^2+1)(x^4+1)\ldots\left({x^2}^{2007}+1\right)$ and $g(x)\left({x^2}^{2008}-1\right)= f(x)-1$.
Find $g(2)$
This is a PRMO level question of functions and I tried it with substituting values also but to no avail and the solution Of this question is also not available thought answer is given as $g(x)=2$.

Some hints:
Note that
$$f(x)(x-1) = x^{2^{2008}}-1$$
This gives $f(2)$.
Now, use this in
$$g(x)\left({x^2}^{2008}-1\right) = g(x)f(x)(x-1)= f(x)-1$$
to evaluate $g(2)$.
