I think it will really help you to write out what it means for to be continuous.

To write math you have to use the "tex" tags. Or if you use the advanced posting (there's a button), just click on the [\tex]\sigma[tex] button to add the tags. Here is how some math might look like

Use

d^*(f,g) = \int_a^b |f(t)-g(t)|\; dt for

I: (X,d^*) \to (R,d) for .

Just to speed things up somewhat, I've written what it means for to be continuous. Only look at the spoiler if you are stuck at this step.

Spoiler: