Question

Give an example to illustrate how the intermediate value theorem no longer holds if the functions are not required to be continuous?

Answer 1

If the functions are not continuous, then there is some f(c) in the interval I = [a,b] that has absolutely no value.

Answer 2

f(x) = x - 2; x<3
f(x) = x^2; x>5

This function has no value between 3 and 5