Let f : [– π π /3, 2 π π /3] → → [0,4] be a function define…

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

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Let f : [– π π /3, 2 π π /3] → → [0,4] be a function defined as f(x) = sin x – cos x + 2. Then f -1 (x) is given by

sin -1

+ cos -1

None of these

Text Solution

Verified by Experts

The correct answer is:

f(x) = sin x – cos x + 2 = 2 sin + 2.

Since f(x) is one-one and onto, f is invertible.

Now fof -1 (x) = x

⇒ ⇒ 2 sin + 2 = x ⇒ ⇒ sin = – 1 ⇒ ⇒ f –1 (x) = sin –1 , because ≤ ≤ 1 for all x ∈ ∈ [0, 4]

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