Question

Choose the correct option from the given alternatives :

If g is the inverse of function f and f'(x) = `(1)/(1 + x)`, then the value of g'(x) is equal to :

विकल्प

• 1 + x⁷ 

• `(1)/(1 + [g(x)]^7`

• 1 + [g(x)]⁷ 

• 7x⁶ 

Answer 1

1 + [g(x)]⁷
[Hint : Since g is the inverse of f, f^–1(x) = g(x)
∴ f[f^–1(x)] = f[g(x)] = x

∴ `f'[g(x)]."d"/"dx"[g(x)]` = 1

∴ f'[g(x)] x g'(x) = 1

∴ g'(x) = `(1)/(f'[g(x)]), "where"f'(x) = (1)/(1 + x^7)`

∴ g'(x) = 1 + [g(x)⁷].