I'm having difficulty understanding how you're supposed to do inverse mapping of a function. Here's the question I think if I see how this is supposed to be done, I'll be able to tackle the rest

The functionn f:(R,T)->(R.S), is given by f(x)=1 if x is an element of [2,3) and f(x)=0 otherwise,

Is f continuous if T=S= Sorgenfrey Topology.