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Let X and Y be sets, f be the function f : X → Y, and x be some member of X. Then the image of x under f, denoted f(x), is the unique member y of Y that f associates with x.
The image of a subset A ⊆ X under f is the subset of Y defined by f[A] = {y ∈ Y | y = f(x) for some x ∈ A}.