Let f(x) = max{x,0} for all x belonging to R and f(xy) is not equals to f(x) f(y), then show that x <0 , y<0
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1 Answers
11Let x>0, then f(x)=x, if y is also positive then f(xy)=xy=f(x)f(y).
If x>0 and y<0 then f(y)=0
But f(x)=x, so f(xy)=0, again that satisfies the eqn, so only alternative is both x,y <0.
