Question

f(x)={x if -pi/2 13 years ago

Answer 1

I don't think it is odd.
A function is odd if f(-x) =-f(x) for each x in the domain of f.
This implies that the domain should be centered around 0 (or that is consists of all real numbers).
Here, f(pi) = 0, while f(-pi) is not even defined. So f cannot be odd.

Answer 2

On the other hand, this function is symmetric in x = pi/2, which means that f(pi/2 -x) = f(pi/2 + x), for every x in the domain.