If f (x) = 2 [x] + cos x, then f: R → R is: (where [ . ] de…

Maths Functions, Limits, Continuity and Differentiability General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 11, 2026

If f (x) = 2 [x] + cos x, then f: R → R is: (where [ . ] denotes greatest integer function)

one − one and onto

one − one and into

many − one and into

many − one and onto

Text Solution

Verified by Experts

The correct answer is:

f(x) = 2[x] + cos x ;f(x) = cos x x ∈ [0, 1)

= 2 + cos x x ∈ [1, 2)

= 4 + cos x x ∈ [2, 3)

= 6 + cos x x ∈ [3, 4)

for x ∈ [0, 1) f ′ (x) = – ve

x ∈ [1, 2) f ′ (x) = – ve

x ∈ [2, 3) f ′ (x) = – ve

x ∈ [3, 4) f ′ (x) = + ve

⇒ function is not one-one

if x ∈ [0, 1) range : [1, cos 1)

x ∈ [1, 2) range : [2 + cos 1, 2 + cos 2)

not onto function

──────────────────────────────────────────────────────────────────────────────────────────

Previous Question Next Question

Get practice questions, solutions, and test series in one place.

Share your experience with this question and solution.

Send your comment, doubt, correction, or feedback to admin.

What students say about this solution

No reviews yet. Be the first to write a review.