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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

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The correct Answer is:
A
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
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  4. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is

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  11. In the following, [x] denotes the greatest integer less than or equal ...

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  12. If f(x)=min.(1,x^2,x^3), then

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  19. If the function g(x)={{:(,k sqrt(x+1),0 le x le3),(,mx+2,3lt xle5):...

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  20. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

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