Where is the function f(x) discontinuous? f(x) = (x^2-x-2)/(x-2), if x is not 2 f(x) = 1, if x=2

For a function to be continuous, the values of the lateral
limits have to be equal and they are equal to the value of function, if we'll let x to
be equal to the value of accumulation point.

We'll
calculate the lateral limits, if x approaches to 2 from the left and from the
right:

lim (x^2-x-2)/(x-2) = lim (x-2)(x+1)/(x-2) = lim
(x+1) = 2+1 = 3

Now, we'll evaluate the limit if x =
2.

According to enunciation, f(2) =
1.

We notice that the limit of the function, if x
approaches to 2, is not equal to the value of the function
f(2).

The function is discontinuous at x =
2.