Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Let ƒ(x) = (log (1 + x)) –1 – x –1 , x > 0, then
Text Solution
Verified by ExpertsThe correct answer is:
C
Consider g(x) = log (1 + x) on the interval [0, x].
Since g(x) is differentiable on (0, x), therefore by Lagrange’s mean value theorem, there exists c ∈ (0, x) such that
= g ′ = 
⇒ 
= 
< 1 … (1)
⇒ log (1 + x) < x ⇒ ƒ(x) > 0
Also, c ∈ (0, x) ⇒ c < x ⇒ 
> 
⇒ 
> 
[By (1)]
⇒ log (1 + x) > 
⇒ 
< 
⇒ 
< 1 + 
⇒ 
– 
< 1
⇒ ƒ(x) < 1.
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