Continuity and DifferentiabilityHard

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 to

Options

A.
B.
C.
D.None of these

Solution

Given that g-1(x) = f(x)
⇒  x = g(f(x))  or  g′(f(x)) f′(x) = 1
⇒  g′(f(x)) =
⇒  g″(f(x)) . f′(x) =
⇒  g″(f(x)) = -

Create a free account to view solution

View Solution Free
Topic: Continuity and Differentiability·Practice all Continuity and Differentiability questions

More Continuity and Differentiability Questions

The differential coefficient of sin−1 w.r.t cos−1 is -...If x = y log xy, then dx/dy equals-...If ƒ(x) = ex g(x), g(0) = 2, g′(0) = 1, then ƒ′(0) is-...Let f(x) = where [x] denotes the greatest integer function. Then -...If y = log , then dy/dx equals-...