Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

$f(x)=\frac{\sin^3x}{[\frac{x}{π}]+\frac{1}{2}}$, where [·] denotes the greatest integer function is (if x is not integral multiple of π)

Options:

odd function

even function

neither odd nor even

both odd and even

Correct Answer:

even function

Explanation:

$f(-x)=\frac{\sin^3x}{[\frac{x}{π}]+\frac{1}{2}}=\frac{-\sin^3x}{-1-[\frac{x}{π}]+\frac{1}{2}}=\frac{\sin^3x}{\frac{1}{2}+[\frac{x}{π}]}=f(x)$