2Let f : R → R be defined by f(x) =then f-'(14, 7[) isNone of the choices[2,3[ and f is not continuous]2,3[ and f is continuousO ]2,3] and f is not continuousLet X be an infinite set with the...

Extracted text: 2x – 1, r< 2="" |="" 2x="" +="" 1,="" r="">2 Let f : R → R be defined by f(x) = then f-'(14, 7[) is None of the choices [2,3[ and f is not continuous ]2,3[ and f is continuous O ]2,3] and f is not continuous Let X be an infinite set with the finite closed topology T={S subset of X; X-S is finite}. Then * (X,T) is homeomorphic to (X,T1) where T1 is the finite closed topology on X None of the choices O (X,T) is not T1 space Every infinite subset of X is dense in X Let T_us be the usual topology on R and T_II gy generated by the unions of {]a,b]/ `ER;asb}. Define f be the lower limit to the mapping from (R, T us) into (R, T II) by