Is it possible to have two one-sided limits but no limit

Question

I am answering a true or false question

Answer 1

          x, if x < 1

f(x) =

          x²+2, if x≥ 1

 

lim_x→1^- f(x) = 1

 

lim_x→1⁺ f(x) = 3

 

So, the one sided limits both exist, but lim_x→1f(x) does not exist since the one sided limits are different.