How do you do problems like this? Im super confused? PLEASE SHOW YOUR WORK!

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

and show every step!

Thank you!

Answer 1

From the left:

1/ (x-2) at x=1

1/ (1-2) = 1/-1 = -1

From the right:

2x-3 at x=1

2(1)-3 = -1

Since these values are equal, the function is continuous.