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If f:R rarr (0,oo)be a differentiable f...

If `f:R rarr (0,oo)`be a differentiable function `f(x)` satisfying
`f(x+y)-f(x-y)=f(x)*{f(y)-f(y)-y}, AA x, y in R, (f(y)!= f(-y) " for all " y in R)` and `f'(0)=2010`.
Now, answer the following questions.
Which of the following is true for `f(x)`

A

`f(x)` is one-one and into

B

`{f(x)}` is non-periodic, where `{*}` denotes fractional part of `x`.

C

`f(x)=4` has only two solutions.

D

`f(x)=f^(-1)(x)` has only one solution .

Text Solution

Verified by Experts

The correct Answer is:
B
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