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

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 also say 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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Answer #1

(a) is false and (b) is true

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