Prove that f is continuous

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1. Let A ⊆ R be a set, and let f: A → R be a function. Prove that if f is monotone and injective, then f is strictly monotone.

2. Let (a, b) ⊆ R be a non-degenerate open bounded interval, and let f: (a, b) → R be a function. Suppose that f is continuous, strictly increasing and bounded. Let F:[a, b] → R be defined by

Prove that F is continuous.

Reference no: EM131067676

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