# Is Differentiation as a system, is an invertible system?

is the following system invertible?

as I understand it, invertible means finding an inverse function which should return back the original input from an output of the given system.

if so I understand correct. Then one could say, yes the system is invertible and the inverse function is

but for example, If our original input is x + 3 then its derivative is 1,
and if I try to use the inverse function it returns x + c.

is the nature of not knowing what exactly c equals makes the system non-invertible; meaning the original input cannot be restored. Does that make the system non-invertible

Basically, the differentiation of $$f(t)$$ and $$(f(t) + c)$$ is indistinguishable $$f^{'}(t)$$, which makes the system, many-to-one, and hence non-invertible.