Pre-image
the original figure
In mathematics, the pre-image of a subset S of the range of a function f is the set of all points in the domain that map to points in S under the function. In other words, it is the set of all input values that will be mapped to the given output values in S.
Symbolically, if f: X → Y is a function and S ⊆ Y is a subset of the range of f, then the pre-image of S under f is defined as:
f^{-1}(S) = {x ∈ X : f(x) ∈ S}
Thus, f^{-1}(S) is a set of all x values in the domain X of the function f such that the corresponding f(x) values are in the given set S.
The pre-image is an important concept in mathematics, especially in functions and transformations. It is used to determine the inverse function of a given function and also helps us to understand the behavior of functions.
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