$a \in \mathbb{R}$

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

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

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][1]  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][2] too, but again, didn't worked very well.


  [1]: http://en.wikipedia.org/wiki/Fourier_transform
  [2]: http://en.wikipedia.org/wiki/Z-transform