Provide an appropriate response.Give an example of a function f(x) that is continuous at all values of x except at , where it has a removable discontinuity. Explain how you know that f is discontinuous at and how you know the discontinuity is removable.

Question

What will be an ideal response?

Answer 1

Let f(x) =  be defined for all x ? 4. The function f is continuous for all   The function is not defined at  because division by zero is undefined; hence f is not continuous at . This discontinuity is removable because   (We can extend the function to  by defining its value to be 1.)