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If g(x) is the inverse of f(x) and f'(x)...

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

A

sec x

B

`sec [g(x)]`

C

`cos[g(x)]`

D

`-sin[g(x)]`

Text Solution

Verified by Experts

The correct Answer is:
B
Since, g(x) is the inverse of f(x).
`:." ""fog(x)"=ximpliesf(g(x))=x`
On differentiating both sides w.r.t. x, we get
`f'{g(x)}.g'(x)=1`
`:." "g'(x)=(1)/(f{g(x)})=(1)/(cos{g(x)})=sec{g(x)}`
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