Problem 1: For each of the following, answer True or False. Give a one sentence justification or a counterex- ample; a counterexample requires no additional justification or explanation. (a) There exist at least two functions f defined on R such that f(f(x)) = x for all x e R. (b) There exists a continuous function f defined on R such that F(x) = f(t) dt has a vertical cusp. (c) Suppose f (x) is injective and defined on R. Then F(x)= f(t) dt is injective.

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A: We the continuity of f to show that f has unique fixed point

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