The integral equation $\int_{-\infty}^{\infty}f(x) + af(g(x)) dx = b$

Question

How to solve for $f(z)$ in the equation $\int_{-\infty}^{\infty}f(x) + af(g(x)) dx = b$ where

1) $f(x),g(x)$ are holomorphic near the real line.

2) $x$ is considered real here.

3) $a$ is a given real and $b$ is a given complex.