Question

Let f(x)=x2+x−6x−2. Note that f(x) is undefined at x=2. However, in this case, we can find a continuous function g(x) defined at x=2 that agrees with f(x) near x=2. Find the function g(x) that is equal to f(x) when x≠2 such that
g(2)=limx→2f(x).

Answer 1

You must have a typo.
I read your function as
f(x) = x^2 - 5x - 2, which is defined for all values of x

to be undefined there must have been a denominator of (x-2)

Answer 2

it's f(x)=x^2+x−6 / x−2
and the answer is: x + 3