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If f(g(x)) = x and g(f(x)) = x then g(x)...

If f(g(x)) = x and g(f(x)) = x then g(x) is the inverse of `f(x) . (g'(x))f'(x) = 1 implies g'(f(x))=1/(f'(x))`
Let us consider a real value bijective function g(x) sun that g'(x) = `sin^2 (x+pi/4) +2 cos (x -pi/4) and g(pi/4) =3` then value of `(g^(-1))(3)` is

A

`1/5`

B

`1/2`

C

`1/3`

D

0

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The correct Answer is:
D
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