Suppose

g(x)={1/(x-2) if x<1
{2x-4 if x≥1

The best description concerning the continuity of g(x) is that the function:
is continuous.
has a jump discontinuity.
has an infinite discontinuity.
has a removable discontinuity.
None of these

To determine the continuity of g(x), we need to check if the function is continuous at every point within its domain.

The first condition we need to consider is if the function is continuous at x=1. We can evaluate the left and right limits of g(x) at x=1 to check for continuity.

For the left limit, as x approaches 1 from the left (x < 1), g(x) approaches 1/(x-2). However, division by zero is undefined, so the left limit is not defined at x=1.

For the right limit, as x approaches 1 from the right (x ≥ 1), g(x) is defined as 2x-4. The right limit evaluates to 2(1)-4 = -2.

Since the left limit and right limit do not match at x=1, g(x) has a jump discontinuity at x=1.

Therefore, the best description concerning the continuity of g(x) is that the function has a jump discontinuity.