Question: Could someone please check my work? Given The following function, find an open interval in the codomain so that the inverse image of That interval

Could someone please check my work?

Given The following function, find an open interval in the codomain so that the inverse image of That interval is nor open f ( x ) = 0, (-00, 0] 1 . (0, 2] - not open 3 , (2, 00 ) Let E = smallest interval around 1 : f - ( 10 , 2] ) = ( 1 - 8, 1+ 8 ) f (o) = 0 which doesn't fell in This open interval centered at 1 Hence, f is discontinuous at o

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