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Let f(x) be a polynominal one-one functi...

Let f(x) be a polynominal one-one function such that
`f(x)f(y)+2=f(x)+f(y)+f(xy), forall x,y in R-{0}, f(1) ne 1, f'(1)=3.`
Let `g(x)=x/4(f(x)+3)-int_(0)^(x)f(x)dx,` then

A

(a) g(x)=0 has exactly one root for `x in (0,1)`

B

(b) g(x)=0 has exactly two roots for `x in (0,1)`

C

(c) `g(x) ne 0, x in R-{0}`

D

(d) `g(x)=0, x in R-{0}`

Text Solution

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The correct Answer is:
D
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