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Part CCSIR NET June 2024monotone-does-not-mean-onto

Monotone does not mean onto

Let f:R→Rf : \mathbb{R} \to \mathbb{R} be a continuous and one-to-one function. Which of the following statements are necessarily true?

  1. A.f is strictly increasing
  2. B.f is strictly decreasing
  3. C.f is either strictly increasing or strictly decreasing✓ Correct
  4. D.f is onto

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests converse assumed.

See pricing

50 are analysed free — try those first.

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

More on this topic

The chapter behind this: Continuity vs uniform continuity vs Lipschitz — free to read

From Continuity and Differentiation › Continuity, uniform continuity, Lipschitz

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

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