Part CCSIR NET December 2023injective-continuous-implies-monotone

Injective continuous implies monotone

Let $f : R \to R$ be a continuous function such that |f(x) − f(y)| ≥ log(1 + |x − y|) for all $x, y \in R$ . Which of the following statements are true?

A.f is necessarily one-one.
B.f need not be one-one.
C.f is necessarily onto.
D.f need not be onto.

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The trap it tests

Converse assumed

The theorem runs one way. You used it in the other.

Drill statements like this

Related counterexample: Continuous on a bounded interval ⇒ bounded

Injective continuous implies monotone

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