Let f: (-1, 1) → R be a differentiable function with f(0) = 1 and f'(0) = -1. If g(x) = (f(nf(x) – n))^n, where n is a natural number and g'(0) = 4, then n equals

Option 1 - 0

Option 2 - 1

Option 3 - 2

Option 4 - 4

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Answered by

Vishal Baghel | Contributor-Level 10

5 months ago

Correct Option - 3

Detailed Solution:

g (x) = (f (nf (x) – n)?
g' (x) = n (f (nf (x) – n)? ¹ . f' (nf (x) – n) . n . f' (x)
∴ g' (0) = 0
⇒ 4 = n (f (nf (0) – n)? ¹ . f' (nf (0) – n) . nf' (0)
⇒ 4 = n (f (0)? ¹ . f' (0) . nf' (0)
⇒ 4 = n . 1 . (-1) . n (-1)
n² = 4
⇒ n = 2

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