Explain why or why not 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 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 in (a, b) such that f(c) = (f(a) + f(b))/2.
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