Question

In half range cosine Fourier series, we assume the function to be _________

(a) Odd function

(b) Even function

(c) Can’t be determined

(d) Can be anything

This question was posed to me during an online exam.

I'd like to ask this question from Fourier Half Range Series topic in division Fourier Series of Engineering Mathematics

Answer 1

The correct option is (b) Even function

To explain I would say: In half range Fourier series expansion, the nature of the function in half of its period is only known. So when we find half range cosine series, there are only cosine terms which imply that the function is even function. f(x) = f(-x).