Final answer:
As x approaches 2, f(x) = 1/(x-2) approaches infinity or negative infinity, depending on whether x is greater than or less than 2.
Step-by-step explanation:
For the function f(x) = 1/(x-2), when x is close to 2, the function's value will approach infinity or negative infinity, depending on the direction from which x is approaching 2. If x approaches 2 from the right (x > 2), f(x) will become a very large positive number. Conversely, if x approaches 2 from the left (x < 2), f(x) will become a very large negative number. This behavior is due to the fact that as x gets closer to 2, the denominator of the function (x-2) becomes very small, which makes the value of the fraction very large in magnitude.