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Function Preimage

Last updated Nov 1, 2022

# Definition

Let $X, Y$ be Sets and let $f: X \to Y$ be a Function. Suppose $A \subset Y$. Then the Function Preimage of $A$ under $f$, denoted $f^{-1}(A)$, is defined $$f^{-1}(A) := {x \in X : f(x) \in A}.$$

# Properties

  1. Function Preimage preserves Elementary Set Operations