thats the bit where I get worried.
Im thinking if you know there is cts bijection and cts inverse when you didnt place any restriction on your domain, then when you do place those restrictions, then it will still map the same, just excluding that point. The thing that gets me a little weird is i just keep seeing in my head a straight line thats not defined at a point thus it cant be cts. But i guess its okay since if you think of 1/x that is a cts function at all points that it is defined on R...
im so bad at this stuff