Question

If $f(x)$ is an odd periodic function with period 2, then $f(4)$ equals

• A. 0
• B. 2
• C. 4
• D. – 4

Answer 1

Answer: (A)

0

Answer 2

Given, $f(x)$ is an odd periodic function. We can take $\sin x,$ which is odd and periodic.

Now since, $\sin x$ has period = 2 and $f(x)$ has period = 2.

So, $f(x) = \sin(\pi x) \Rightarrow$ $f(4) = \sin(4\pi) = 0$.