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A function f : R to R satisfies the equ...

A function `f : R to R` satisfies the equation `f(x+y) = f (x) f(y), AA x, y ` in R and `f (x) ne 0` for any x in R . Let the function be differentiable at x = 0 and f'(0) = 2. Show that` f'(x) = 2 f(x), AA x ` in R. Hence, determine f(x)

A

f(x)

B

`-f(x)`

C

2f(x)

D

None of these

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