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Let f x = x 2 - 4 x - 3 , x > 2 and g ( x ) be the inverse of f ( x ) . Then the value of 1 g ' ( 2 ) , where f ( x ) = 2 , is (here, g ' represents the first derivative of g )

Correct answer

6

Step-by-step solution

As g ( f ( x ) ) = x ( ∵     g ( x ) = f − 1 ( x ) ) Differentiating, we get, g ' ( f ( x ) ) f ' ( x ) = 1 ⇒ g ' ( f ( x ) ) = 1 f ' ( x ) when f ( x ) = 2 ⇒ x 2 − 4 x − 3 = 2 ⇒ x = 5 ,     x = − 1 ∵ x > 2 ∴     x = 5 g ' ( 2 ) = 1 ( 2 x − 4 ) x = 5 = 1 6

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