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If f : R rarr (0, oo) is a differentiabl...

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

A

2016

B

2014

C

2012

D

2010

Text Solution

Verified by Experts

The correct Answer is:
D
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