Could someone please check my work

what happens to D under f ? let fid + RR be continuous. For each of the following, prove or give a counterexample . 1. If D is open, Then fCD) is open. counterexample : f (x) = 1* 1 Continuous functions don't D = ( - 1, 1 ) which is open necessarily map open Sets f ( D ) = [0, 1) which is neither To open Sets. closed or open 2. If D is closed, Then f CD) is closed. Counterexample: f (x ) = x241 Continuous functions don't necessarily D = R which is closed ( and unbounded , so not Compact ) Map closed Sets f(D ) = (0 , 1] which is To closed sets, neither closed or open 3. If D is not open, Then f CD) is not open. Counterexample: f (x ) = 1x 1 Continuous functions D = [1 , 1 ) which is neither open or don't necessarily map closed not open Sats To f (D ) = [0, 1] which is not open , in particular it is not open SETS. closed