COnsider g(x)=(8)/(x-6) on (6,13)
(a) Is this function continuous on the given interval? If it is continuous, type "continuous". If not, give the x -value where the function is not continuous.
Is is continous? If not? what interval then?
when x=6, you would be dividing by zero
so it is discontinuous at x=6
in general, a discontinuity will result when a division by zero results or an even root of a negative number is attempted, such as the square root, fourth root, sixth root etc.
To determine if the function g(x) = 8 / (x - 6) is continuous on the given interval (6, 13), we need to check three conditions:
1. The function must be defined on the entire interval.
2. The limit of the function as x approaches the endpoints of the interval must exist.
3. The value of the function at the endpoints must equal the limits.
In this case, g(x) is undefined when x = 6 because the denominator becomes zero. Therefore, g(x) is not defined at x = 6, which means it is not continuous at this point.
To find the interval on which the function is continuous, we need to exclude x = 6 from the interval (6, 13). So the continuous interval for the function g(x) is (6, 13] or (6, 13)∪(6, 13].
Let me know if you need help with anything else!