In this question, we are going to call a function, f : R ? R,type A, if ?x ? R, ?y ? R such that y ? x and |f(y)| ? 1. We alsosay that a function, g, is type B if ?x ? R such that ?y ? R, if y? x, then |f(y)| ? 1.
Prove or find a counterexample for the following statements.
(a) If a function is type A, then it is type B.
(b) if a function is type B, then it is type A.
