Determine whether the following statements are true and give an explanation or counterexample.

(a) If a function is left-continuous and right-continuous at a, then it is continuous at a.

(b) If a function is continuous at a, then it is left-continuous and right-continuous at a.

(c) If a < b and f(a) L f(b), then there is some value of c in (a, b) for which f(c) = L.

(d) Suppose f is continuous on [a, b]. Then there is a point c (a, b) such that f(c) = (f(a) + f(b)) / 2