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A function f : R rarr R satisfies the eq...

A function `f : R rarr R` satisfies the equation `f(x + y) = f(x) . f(y)` for all, `f(x) ne 0`. Suppose that the function is differentiable at x = 0 and f'(0) = 2. Then,

A

f'(x) = 2f(x)

B

f'(x) = f(x)

C

f'(x) = f(x) + 2

D

f'(x) = 2f(x) + x

Text Solution

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The correct Answer is:
A
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