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Q.

If R→R is continuous such that f(x+y)=f(x)+f(y),∀ x∈R,y∈R and f(1)=2 then f(100)=

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a

100

b

50

c

200

d

0

answer is C.

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Detailed Solution

f(x+y)=f(x)+f(y), f(x)=ax⇒f(1)=2⇒a=2 f(x)=2x⇒f(100)=200

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