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Let \(f:X \to Y\) be a function and \(A, B \subseteq X\) be subsets of the domain.

  1. Is \(f(A \cup B) = f(A) \cup f(B)\text{?}\) Always, sometimes, or never? Explain.

  2. Is \(f(A \cap B) = f(A) \cap f(B)\text{?}\) Always, sometimes, or never? Explain.

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