Let be any function defined on R and let it satisfy the condition : f(x)-f(y)≤|x−y2|,∀x,y∈R If f0=1, then

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fx>0,∀x∈R

fx<0,∀x∈R

fx=0,∀x∈R

fx can take any value

answer is A.

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Detailed Solution

limx→yfx−fyx−y≤limx→yx−y⇒f1y≤0,∀y ⇒f1x=0,∀x ⇒fx=c for all x, since f(0)=1 ⇒c=1 f(x)= 1 >0 for all x.

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