Final answer:
The function g(x) exhibits discontinuity at x = 1, because the value from the left as x approaches 1 is 1/2 and the value from the right at x = 1 is 1. Thus, g(x) is continuous for all x except at x = 1.
Step-by-step explanation:
The continuity of a function g(x) refers to the function being unbroken or uninterrupted at all points in its domain. In the case of the given function g(x), we have two separate rules defining g(x): one for x < 1 and the other for x ≥ 1. To analyze continuity at x = 1, we need to check not only if both rules give the same value at x = 1 but also if the function approaches the same value from either side of x = 1.
For x < 1, g(x) is defined as 1/(x+1). As x approaches 1 from the left, g(x) approaches ½. For x ≥ 1, g(x) is defined as 2x - 1. When x = 1, g(x) = 2(1) - 1 = 1. Thus, there is a discontinuity at x = 1, since the limits from the left and the right do not agree. Therefore, the best description concerning the continuity of g(x) is that g(x) is continuous for all x except at x = 1.