It's easy to solve for $x$ in this equation: $$y=x-f(x)-1$$ where $f(x)$ is a different function than y, but I need to solve for $x$ without $f(x)$ on the other side. How would I accomplish this? Also, does it matter the technique used to solve this what $f(x)$ is?
If it is not possible without knowing what the function is, for my uses it is a version of $\pi(x)$, the prime counting function, only defined for composites. So, that is, what is the inverse of the function $x-f(x)-1$ where $f(x)$ is $\pi(x)$ only defined for composite numbers?