I am trying to figure out how to calculate the inverse of a function that is the product of two different powers. I first tried finding the inverse of a simpler case: $$f(x)=(1+x)^a\cdot(1+b\cdot x)^c$$ With restrictions: $$a\in \mathbb{R}$$ $$ 0<a<1$$ $$c\in \mathbb{R}$$ $$0<c<1$$
But I have no idea where to start, wolfram alpha says "no result found in terms of standard mathematical functions" and sympy says "No algorithms are implemented to solve equation." Is this equation impossible to invert?