Let $ f: \Bbb R \to \Bbb R $ be a function that satisfies the following property $$f(x+\pi)=-f(x),\ \text{for all $x\in\Bbb R$.}$$
Show that all Fourier coefficients of subscript pa are null.
Use this result to find the Fourier series of the function $ f (x) = x $ if $ 0 \le x \le \pi $, $ f (x + \pi) = - f (x) $ for all $ x \in \Bbb R $.
I already did the test that the even subscript coefficients are null. The question at this point, which I don't know if it will be wrongly stated, is that how do I apply this exercise to find the series if $ f (x) = x $ does not satisfy that $ f (x + \pi) = - f (x) $. Can someone help me with that particular piece?