$a \in \mathbb{R}$

$f:\mathbb{R} \rightarrow \mathbb{R}$

$g:\mathbb{R} \rightarrow \mathbb{R}$

For generic functions $f$ and $g$, how isolate $f(x)$ in the equation below?

$f(x+a)=f(x)+a\times g(x)$

I tried to use Fourier Transform and Inverse Fourier Transform but looks like this don't work very well.

$f(x - a)=$ $e^{-2\pi i a \xi} \hat{f}(\xi)$

$\hat{f}(\xi)=$
$\int_{-\infty}^{\infty}f(x) e^{-2\pi i x\xi}\, dx \quad$
*(Fourier Transform)*

I tried ZTransform too, but again, didn't worked very well.

`f`

or $f(x)=\cdots$, where $\cdots$ is something using $g$ and $a$. $\endgroup$ – GarouDan Oct 31 '11 at 23:02