Web Definition: Image
The image of an element x ∈ X under the function f : X → Y, denoted by f, is the unique y ∈ Y that is associated with x. The image of a subset A ⊂ X under f is the subset of Y defined by Notice that the range of f is the image f of its domain X Note that with this definition, the direct image f becomes a function whose domain is the set of all subsets of X & whose codomain is the power set of Y Note that the same notation is used for the original function f & its direct image. This is a common convention; the intended usage must be inferred by context. The preimage or inverse image of a set B ⊂ Y under f is the subset of X defined by Note that f −1 should not be confused with the inverse function. The two only coincide if f is bijective. f −1 is a new function whose domain is the power set of Y & whose codomain is the power set of X 1. {1,2,3} → {a,b,c,d} defined by In this example, the image of {2,3} under f is f = {c, d} & the range of f is {a, c, d}. The preimage of {a, b} is f −1 = {1}. 2.
Read More »Dictionary Entry: An imitation, representation, or similitude of any person, thing, or act, sculptured, drawn, painted, or otherwise made perceptible to the sight - a visible presentation - a copy - a likeness - an effigy - a picture - a semblance. To represent or form an image of - as, the still lake imaged the shore - the mirror imaged her figure.
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