GATE IN 2022 | Question: 3

Question

A periodic function $f(x),$ with period $2,$ is defined as

$f(x) = \left\{\begin{matrix} -1 -x & -1 \leq x < 0 \\ 1 – x & 0 < x \leq 1 \end{matrix}\right. $

The Fourier series of this function contains ___________

• A. Both $\cos (n \pi x)$ and $\sin (n \pi x)$ where $ n = 1, 2, 3, \dots $
• B. Only $\sin (n \pi x)$ where $ n = 1, 2, 3, \dots $
• C. Only $\cos (n \pi x)$ where $ n = 1, 2, 3, \dots $
• D. Only $\cos (2n \pi x)$ where $ n = 1, 2, 3, \dots $