If g is the inverse of f and f ¢(x) = sin x then g¢(x) = | MATH - ROLLE'S THEOREM, LAGRANGE'S MEAN VALUE THEOREM | SolveeIt | Solveeit

Today, August 23

Question

If g is the inverse of f and f ¢(x) = sin x then g¢(x) =

A

– cosec (g (x))

B

sin (g (x))

C

cosec (g(x))

D

None

Answer

cosec (g(x))

Explanation

Solution

y = g(x) = f^–1(x)

\ fog (x) = x

̃ f ¢ (g(x)) × g¢(x) = 1

̃ g ¢ (x) = $\frac{1}{f'(g(x))}$

= $\frac{1}{\sin(g(x))}$ = cosec g ((x))