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Suppose f and g are differentiabel funct...

Suppose f and g are differentiabel functions such that `xg (f(x))f'(g (x))g '(x) =f(g(x))g '(f(x)) f'(x) AA x in R and f` is positive `AA n in R.` Also `int _( 0)^(x) f (g(t )) dt =1/2 (1-e^(-2x))AA x in R, g (f(0))=1 and h (x) = (g(f (x)))/(f (g(x)))AA x in R.`
The graph of `y =h (x)` is symmetric with respect to line:

A

1

B

`e ^(1//3)`

C

e

D

`e ^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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