If f : R → → R where f(x) = ax + cosx is an invertible func…

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

Published by: CGP EDU Academic Team

Published on: August 12, 2026

If f : R → → R where f(x) = ax + cosx is an invertible function then

ae(-2, 1] ∪ ∪ [1, 2)

a ∈ ∈ [-2, 2]

ae[- ∞ ∞ , -1] ∪ ∪ [1, ∞ ∞ )

a ∈ ∈ [-1, 1]

Text Solution

Verified by Experts

The correct answer is:

The function f(x) is clearly on to if a ≠ ≠ 0. Now f '(x) = a − − sinx. f '(x) > 0 ∀ ∀ x ∈ ∈ R

⇒ ⇒ a ≥ ≥ sin x ∀ ∀ x ∈ ∈ R

⇒ ⇒ a ≥ ≥ 1. For f'(x) ≤ 0. ∀ ∀ x ∈ ∈ R

we get a ≤ sin x ∀ ∀ x ∈ ∈ R

⇒ ⇒ a ≤ -1 a ∈ ∈ (- ∞ ∞ , -1] ∪ ∪ [1, ∞ ∞ )

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