Given the equation:
$$ 1= f(x)+f\left(\frac x2\right)+f\left(\frac x3\right)+f\left(\frac x4\right) $$
How could I solve it, or the more general equation:
$$ 1= f(x)+\left(\frac x2\right)+f\left(\frac x3\right)+f\left(\frac x4\right)+\dots+f\left(\frac xN\right) $$
For a given number $N$, could I use Wolfram math online to solve it?

For the case:
$$ 1= f(x)+f(x-2)+f(x-3)+f(x-4) $$
I could find a generating function since it is just a recurrence equation.