Comprehension

निर्देश : निम्नलिखित प्रश्नों के लिए नीचे दिए गए कथनों पर विचार करें:

माना f : (-1, 1) → R एक अवकलनीय फलन है जहाँ f(0) = -1 और f’(0) = 1 माना h(x) = f(2f(x) +2) और g(x) = (h(x))2

h’(0) किसके बराबर है?

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  1. -2
  2. -1
  3. 0
  4. 2

Answer (Detailed Solution Below)

Option 4 : 2
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व्याख्या:

मान लीजिये कि f: (-1, 1)→ R एक अवकलनीय फलन है जहाँ f(0) = -1 और 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

∴ विकल्प (d) सही है।

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