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In this question, we are going to call a function, f : R ? R, type...

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Advance Math

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.

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