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Let $f$ and $g$ be two functions from $[0, 1]$ to $[0, 1]$ with $f$ strictly increasing. Which of the following statements is always correct?

  1. If $g$ is continuous, then $f ∘ g$ is continuous.
  2. If $f$ is continuous, then $f ∘ g$ is continuous.
  3. If $f$ and $f ∘ g$ are continuous, then $g$ is continuous.
  4. If $g$ and $f ∘ g$ are continuous, then $f$ is continuous.
asked in Set Theory & Algebra by Veteran (29.2k points)   | 48 views

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