Finding properties of a real function

Question

Is there a way, using sympy, to figure out (some) properties of a function, thought of as a real function?

For example, if

>>> x = Symbol('x', real=True)
>>> f = Lambda(x, sqrt((x-2)/(x+2)))

then something like

>>> f.domain()
(-oo, -2) U [2, oo)
>>> f.image()  # there is "imageset", but it is not expanding on the set of reals
[0, 1) U (1, oo)
>>> f.is_injective()
True
>>> f.is_bounded()
False
>>> f.is_even  # currently returns None
False

Some of this is implemented in Wolfram Alpha.

Answer 1

Some of these are implemented in sympy.calculus.util and sympy.calculus.singularities, although they aren't exported to from sympy import * yet, so you'd have to import them manually. The functionality for some of them is still limited, so you may not yet get an answer.