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Let f(x) be a function such that f(x).f(...

Let `f(x)` be a function such that `f(x).f(y)=f(x+y)`, `f(0)=1`,`f(1)=4`. If `2g(x)=f(x).(1-g(x))`

A

g(x) - g(1-x) = 0

B

g(x) = 1- g(1-x)

C

`underset(k = 1)overset(9)sumg((k)/(10)) = (9)/(2)`

D

`underset(k = 1)overset(18)sum g((k)/(19)) = 9`

Text Solution

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The correct Answer is:
B, C, D
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