I came up with a theorem.
Define a
super function to be a function defined for all real numbers that is made out of sum/difference or product (not quotient) or composition of: sines,cosines,exponentials,polynomials.
For example,
is a super function. Also
is a super function. But
is not because
is not one of the basic functions on the list and also because division is not allowed in this defintion.
Theorem: Let
be a finite interval and let
be a super function. Then unless
is identically zero the equation
has only
finitely many solutions on the interval
.