I want to define some basic functions known from "discrete analysis":
$$I(f)(x):=f(x)$$ $$E(f)(x):=f(x+1)$$ $$\Delta(f)(x) := (E-I)(f)(x) = f(x+1)-f(x)$$ $$\nabla(f)(x) := (I-E^{-1})(f)(x) = f(x)-f(x-1)$$
And I know that I can define a function f[x_] := x^2
like that, but how can I take a function and evaluate it at the given position like E[fn_] := evaluate fn at x+1
?