elementary superfunctions

[BenStandeven]

It should be noted that superfunction is not unique in most cases. For example, for
\( f(x)=2 x^2-1 \), superfunction is \( F(x)=\cos(2^x C) \)

Ya, this is the simple kind of non-uniqueness, its just a translation along the x-axis.
However there are also more severe types of non-uniques, as I already introduced in my first post, we have two solutions (which are not translations of each other):
\( F(x)=\cos(2^x) \) and \( F(x)=\cosh(2^x) \).

Actually, \( \cos(2^x) = \cosh(i 2^x) = \cosh(2^{x + \frac{\pi i}{2 \ln 2}}) \), so they are translations of each other, albeit along the imaginary axis instead of the real axis.