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Q.

If f : RR is continuous such that

f(x+y)=f(x)+f(y), x, yR,  f(1)=12, then f(200)

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a

100

b

50

c

200

d

0

answer is A.

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Detailed Solution

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f(x+y)=f(x)+f(y), x, yR, f(x)=kx f1=k=12 f(x)=12x   f(200)=12200=100

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