Test the continuity of the following function at x=2?

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Test the continuity of the following function at x=2. If the function is not continuous at x=2, give a reason why it is not continuous.

g(x)= {4x-3 if x<2
x^2 if x/>2 (x is bigger or equal to 2)

So do I just put in the number? like,

=4(2)-3
=5

and
=(2)^2+1
= 4+1
=5

so the limit does exist. and then what?
 
Since the limit exists at x = 2, the limit is continuous at that point

1) Both right and left side limits exist
2) lim (x-->a) f(x) = f(a)
3) f(x) is defined at that point

At that point, 4x-3 if x<2 is not defined but since x = 2 at: x^2 if x/>2 (x is bigger or equal to 2), that point is considered to be defined
 
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