Question

Determine for what numbers, if any, the given function is discontinuous. f(x) = {x−5 if x≤5x2−10 if x>5

Answer 1

x = 5

Explanation:

Discontinuities arise in function definitions from several sources. One of them is the boundary of the piecewise definition. Here, the boundary is at x=5.

The function is defined to be f(5) = 0, but the limit from above as x approaches 5 is 5²-10 = 15. This value is not equal to zero (the value of f(5)), so there is a discontinuity at that point.