I am wondering if this statement is true:
$x(t)-x(t-a) = f(t)$, where $a$ is a known constant, $f(t) \le M\ \forall t$, $M$ is a known constant, then $x(t)$ is also bounded by some constant. If so, how do we show it?
My initial idea was to use Laplace transform on LHS, but since I do not the exact form of $f(t)$ (but only know that it is bounded $\forall t$), I am not sure how to proceed with that approach.
Any help appreciated. Thanks.
Not true. For example, $x(t) = t$ with any $a$.