2 added math-physics tag, since this more a question of physics than of maths
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# Why is the output of an LTI system the convolution of the input funtion and the impulse response?

I am looking at the description of LTI systems in the time domain.

Intuitively, I'd have guessed it would be the composition of the input function and some "system function". $$y(t) = f(x(t)) = (f\circ x)(t)$$ Where $x(t)$ is the input, $y(t)$ output and $f(x)$ a "system function".

Why is it not that way? Could such a "system function" be found for, say, an R-C-Circuit?

The actual output function y(t), is defined as $$y(t) = (h * x)(t)$$ Where $h(t)$ is the response to a dirac impulse. This is hard to grasp for me. Why is it so? I have looked at various explanations, drawings of rectangles becoming infinitely narrow, which I sort of understood, but it is still "hard to grasp"! I am looking for a simple explanation in one or two sentences here.

http://en.wikipedia.org/wiki/LTI_system_theory