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Maths JEE - Advanced Previous Year Paper JEE-Advanced-2020-Paper-1 Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If the function f : R R is defined by f(x) = |x|(x - sin x), then which of the following statements is TRUE?

f is one-one, but NOT onto

f is onto, but NOT one-one

f is BOTH one-one and onto

f is NEITHER one-one NOR onto

Text Solution

Verified by Experts

The correct answer is:

f(x) is odd, continuous function

for x 0, f’(x) = 2x - sin x - x cos x = x(1 - cos x) + (x - sin x) 0

for x < 0, f (x) = -2x + sin x + x cos x = x(cos x - 1) - (x - sin x) > 0 as x < 0

So f(x) strictly increases in is one-one

So f(x) is onto

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