Thanks for the response.
I think I understand. So, would it make more sense for me to say that the piecewise function isn't discontinuous? Or that the piecewise function is continuous?
And what about my math? Am I going about this the correct way?
Screenshot of my homework problem along with my solution so far. I'm not sure if I'm doing this correctly and if I am... if I'm answering correctly. Thank you. (EDIT: I made 1 small error with the piecewise definition. Ignore the f(x) before g(x).)