Examine f(x) for continuity at x=1 if f(x)=arctan(2)/(x-1) Select one: a. f(x) is continuous at x=1 b. f(x) has an essential discontinuity at x=1 c. It's not possible to examine the function for continuity d. f(x) has a removable discontinuity at x=1 e. f(x) has a jump discontinuity at x=1

To determine the continuity of the function \( f(x) = \arctan\left(\frac{2}{x-1}\right) \) at , we need to analyze the behavior of the function as approaches 1.First, let's rewrite the function in a more convenient form: As approaches 1, the denominator approaches 0, which makes the argument of the arctangent function approach infinity. This indicates that there is a vertical asymptote at .To confirm the type of discontinuity, we can consider the limit of \( f(x) \) as approaches 1 from both sides: Since the left-hand limit and the right-hand limit are not equal, there is a jump discontinuity at .Therefore, the correct answer is:e. \( f(x) \) has a jump discontinuity at .