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Let f be a one-one function such that f(...

Let f be a one-one function such that `f(x).f(y) + 2 = f(x) + f(y) + f(xy), AA x, y in R - {0} and f(0) = 1, f'(1) = 2`. Prove that `3(int f(x) dx) - x(f(x) + 2)` is constant.

A

`f(x)=1-x^(2)`, depends on x

B

`f(x)=1+x^(2)`, independt of x

C

`f(x)=1-x^(4)`, depends on x

D

`f(x)=1+x^(6)`, independent of x

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The correct Answer is:
B
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