Let f(x) = , x ≠ ≠ 1. Then, for what value of α α is f(f(x…

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

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Let f(x) = , x ≠ ≠ 1. Then, for what value of α α is f(f(x))

= x ?

− −

− − 1

Text Solution

Verified by Experts

The correct answer is:

f(x) = , x ≠ ≠ − − 1

f(f(x)) = x ⇒ ⇒ = x

⇒ ⇒ = x ⇒ ⇒ ( α α + 1)x 2 + (1 − − α α 2 ) x = 0 ……(1)

⇒ ⇒ α α 2 − − α α − − 2 = 0

⇒ ⇒ ( α α − − 2) ( α α + 1) = 0 ⇒ ⇒ α α = 2, − − 1

Putting x = 2 in (1)

α α 2 - 2 α α − − 3 = 0

⇒ ⇒ ( α α + 1) ( α α − − 3) = 0 ⇒ ⇒ α α = − − 1, 3

The common solution is α α = − − 1

∴ ∴ is the correct alternative

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