if some function is continuous on some open interval (a,b) then will that function must be continuous on x whereas a

Question

if some function is continuous on some open interval (a,b) then will that function must be continuous on x whereas a<x<b ? also will that function must be continuous on x whereas a<x<b  & [a,b] is closed interval?

turingtest · Answer

you phrased this rather strangely, but if the question is
"if f(x) is continuous on an open interval (a,b) is it continuous on the closed interval [a,b,]?"
the answer is yes at all places except the endpoints

turingtest · Answer

well, it may or may not be continuous at a and b is the point
but in between, yes, it is

anonymous · Answer

sorry I phrased it in a wrong way but thanks for the answer