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Let f and g be differentiable functions ...

Let f and g be differentiable functions satisfying g'(a) = 2 g(a) = b and fog = I (Identity function). Then f'(b) is equal to

A

2

B

`(2)/(3)`

C

`(1)/(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`fog=1`
`{:(implies,fog(x)=1(x)," for all "x),(implies,f(g(x))=x," for all "x),(implies,(d)/(dx)[f(g(x))]=1," for all "x),(implies,(d)/(dg(x))[f(g(x))].(dg(x))/(dx)=1," for all "x),(implies,f'(g(x))g'(x)=1," for all "x):}`
`impliesf'(g(a))g'(a)=1impliesf'(b)xx2=1impliesf'(b)=(1)/(2)`
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