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If g is the inverse of a function f and f ' x = 1 1 + x 5 , then g ' x is equal to

Options

  1. A1 1 + g x 5
  2. B1 + g x 5
  3. C1 + x 5
  4. D5 x 4

Correct answer

B. 1 + g x 5

Step-by-step solution

g is the inverse of f i.e. g x = f - 1 x   ⇒ f g x = x Differentiating both the sides w.r.t x , we get f ' g x . g ' x = 1 ⇒ g ' x = 1 f ' g x as   f ' x = 1 1 + x 5 ⇒ g ' x = 1 1 1 + g x 5   g ' x = 1 + g x 5

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