Question

Let g(x) be the inverse of an invertible function f(x) which is differentiable for all real x, then g"(f(x)) equals

(A) \(- \frac{f"(x)}{(f'(x))^3}\)

(B) \(\frac{f'(x)f"(x)- (f'(x))^3}{f'(x)}\)

(C) \(\frac{f'(x)f"(x)- (f'(x))^2}{(f'(x))^2}\)

(D) none of these

Answer 1

Correct option is (A) \(- \frac{f"(x)}{(f'(x))^3}\)