Final answer:
A function f has a removable discontinuity at x = 5 if the limit of the function as x approaches 5 exists but is not equal to the value of the function at x = 5.
Step-by-step explanation:
A function f has a removable discontinuity at x = 5 if the limit of the function as x approaches 5 exists but is not equal to the value of the function at x = 5. In other words, there is a hole in the graph of the function at x = 5.
To determine if a function has a removable discontinuity at x = 5, you need to evaluate the limit of the function as x approaches 5 from both the left and the right. If the limits exist and are equal, but are not equal to the value of the function at x = 5, then there is a removable discontinuity.
For example, let's say f(x) = (x^2 - 25) / (x - 5). The function is undefined at x = 5 because it results in a division by zero. However, if we simplify the function using algebra, we get f(x) = x + 5. The limit as x approaches 5 is 10, which is not equal to f(5) = 10. Therefore, f has a removable discontinuity at x = 5.