BITSAT 2015 Paper

Since, g is the inverse of function f.
Therefore
g (x) = f−1 (x)
⇒ f [g(x)] = x
⇒ fog (x) = x , for all x
Differentiate both side,w.r.tx
⇒

d

dx

{fog (x)} =

d

dx

(x) . for all x
⇒ f ' [g(x)] g ' (x) = 1 for all x
⇒ sin {g(x)} g ' (x) = 1 for all x
(By defn of f '(x))
⇒ g ' (x) =

1

sin{g(x)}