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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.