Question

how to show the function is continuous at x=-1 and x=2?

Answer 1

Your function is only continuous at x = 2.

\[\lim_{x \rightarrow 2^-} g(x) = 2^2 = 4\]
\[\lim_{x \rightarrow 2^+} g(x) = 2.2^2 - 4 = 4\]
So it is continuous at x=2.

The right side and left side limit at x = -1 are not equal so it is not continuous at x = -1

Answer 2

Is it ,like this ?! i got the same answer, but i was confused when the question asked to show it is continuous at 2 points while its not .thanks @linh412986

Answer 3

You should believe yourself. The method is clear. There only one case that the question is wrong :)

In order to g(x) is continuous at x = -1, g(x) = 2x + 3 when x < -1