f:R†→R be a continuous function satisfying fxy=f(x)−f(y)∀x,y∈R+.If f′(1)=1, then

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f is unbounded

limx→0 f1x=0

limx→0 f(1+x)x=1

limx→0 x⋅f(x)=0

answer is A.

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Detailed Solution

f′(x)=limh→0 f(x+h)−f(x)h=limh→0 f1+hxhxx=f′(1)x=1x⇒f(x)=ln⁡x as f(1)=0

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