Test Index

BITSAT 2015 Paper

Section: Mathematics

Question : 87 of 150

Marks: +1, -0

If g is the inverse of function f and f ' (x) = sin x, then g¢(x) is equal to

Solution:

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

⇒

\frac{d}{dx}

{fog (x)} =

\frac{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) =

\frac{1}{\sin\{g(x)\}}

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