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

Question

If g is the inverse of a function f and f ' x = 1 1 + x 5 , then g ' x is equal to, 1 1 + g x 5, 1 + g x 5, 1 + x 5, 5 x 4

MARKS App · Accepted Answer

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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