Comprehension

Direction : Consider the following for the items that follow :

Let f : (-1, 1) → R be a differentiable function with f(0) = -1 and f’(0) = 1 Let h(x) = f(2f(x) +2) and g(x) = (h(x))2

What is h’(0) equal to? 

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. -2
  2. -1
  3. 0
  4. 2

Answer (Detailed Solution Below)

Option 4 : 2
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NDA 01/2025: English Subject Test
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Detailed Solution

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Explanation:

Let f: (–1, 1)→ R be a differentiable function with f(0) = –1 and f'(0) = 1

⇒ h(x) = f(2f(x) + 2)

⇒ h'(x) = f'(2f(x) + 2)2f'(x)

⇒ h'(0) = f'(2f(0) + 2).2f'(0)

= f'(–2 + 2).2(1)

= f'(0).2 = (1).2 = 2

∴ Option (d) is correct.

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