Question

Which of the following functions is periodic?

• A. f(x) = x - [x] where [x] denotes the largest integer less than or equal to the real number x
• B. $f(x) = \sin \frac{1}{x}$ for $x \neq 0, f(0) = 0$
• C. $f(x) = x \cos x$
• D. none of these

Answer 1

Answer: (A)

f(x) = x - [x] where [x] denotes the largest integer less than or equal to the real number x

Answer 2

Answer (a) f(x) = x - [x] where [x] denotes the largest integer less than or equal to the real number x