Question

Which of the following function is periodic with period $ \pi $ ?

• A. $ f(x)=x\cos x $
• B. $ f(x)=|\cos x| $
• C. $ f(x)=\sin x $
• D. $ f(x)=[x+\pi ] $ Where $ [x] $ means the greater integer not greater than $ x. $

Answer 1

Answer: (B)

(a) $ f(x)=x\cos x $ It is not periodic for any period
(b) $ f(x)=\,|\cos x| $ It is periodic for the period $ \pi $
(c) $ f(x)=\sin x $ It is periodic for the period $ 2\,\pi $
(d) $ f(x)=[x+\pi ] $ It is not periodic with period $ \pi $
$ \therefore $ Option (b) is correct.