How do I solve this problem?

Question

suppose g(x) = { 1/ (x-2) if x<1 }

{2x-3 if x ≥ 1 }

The bet description concerning the continuity of g(x) is that the function?

Can someone please explain how to do this problem in the answer

Thank you!

Answer 1

Since the domain of the top function is x < 1, Take the limit of the top function as x approaches 1 from the left.

Then take the limit of the bottom function as x approaches 1 from the right (domain is x > 1).

If the limits are the same, the function is continuous.

In this case, both limits equal -1 so the piecewise function is continuous.