Monsieur Ejemplé

Give an example of a function f:R^2 --> R s.t. the function is not continuous at zero, but for any (straight) line L passing through the origin, the induced function f|L is continuous on L.

>>4

I don't get it. Maybe I'm misenterpreting the induced function, but that way I see it any straight line through the origin would be 0, except at one point, where it would be one, except in the freak case the line is y=0, then the induced function would be 0 continously.

Am I not quite getting the idea of induced functions? Never met them