Question

Determine the continuity of the function at the given points. f(x) = { 1 x - x-1, for x= 1, for x +1 at x = 1 and x = 1.5 sty 4- 3 - 2 1 -3 2 + 57 O The function f is continuous at neither x=1.5 norx=1. The function f is continuous at x=1.5 but not atx=1. O The function fis continuous at both x=1.5 and x=1. The function fis continuous at x=1 but not atx=1.5.

Answer 1

To verify the continuity of a function we verify that the limit for any point a, is the same in the right limit, and left limit; also the function must be defined at value a.

Since the question is to verify the continuity at x=1 and x=1.5, we can see that there is a hole at x=1 and that the limit is not the same coming from both sides and that it is different from the value in which the function is defined.

At x=1.5 the limit is the same on both sides and the function is defined on the value given which means that the function is continous.

Answer:

The function f is contious at x=1.5 but not at x=1