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Alfonso92
f(x)={x if -pi/2<x<pi/2, pi-x if pi/2<x<3pi/2}, How do I demonstrate that it is an odd function?
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.
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.