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Tushar Watts Grade: 12
        

Ques1) 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.

7 years ago

Answers : (1)

bibhash jha
15 Points
										

f(x) can be written as ,


 


f(x)= o if x<=0


and f(x)=x if x>0


now consider the cases (1)x,y>0  (2) x>0 y<0 or x<0 y>0 (3) x<0 y<0


 


(1) f(xy) = xy


   f(x)f(y)=x.y=xy


so f(xy)=f(x)f(y)


(2)


f(xy)=0 as xy<0


f(x).f(y) = 0 as f(x)=0 or f(y)=0


(3)


f(xy)=xy as xy>0


f(x)=0 and f(y)=0 => f(x)f(y)=0


therefore f(xy)  is not equal to f(x)f(y)

7 years ago
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