Final answer:
The function g(x) = (3x + 1) / (x - 2) is continuous at x = 0 because the denominator does not equal zero at that point, hence the function is defined and continuous there.
Step-by-step explanation:
To determine if the function g(x) = (3x + 1) / (x - 2) is continuous at x = 0, we must examine the behavior of the function at that point. In general, a function is continuous at a point if the limit as x approaches the point from both sides is equal to the function's value at that point.
In this case, g(x) is a rational function, which is continuous everywhere its denominator is not zero. Since the denominator x - 2 is not zero at x = 0 (it is -2), there are no issues of the function being undefined, and thus g(x) is continuous at x = 0.