Image And Preimage Functions. Let x be an element of t t 1 s. Roughly speaking you might think of f x as a kind of distorted copy or image of x in b the preimage f 1 y of y is the set of all things in a that f sends into y.
In words the image f x of x is the set of all things in b that f sends elements of x to. Roughly speaking you might think of f x as a kind of distorted copy or image of x in b the preimage f 1 y of y is the set of all things in a that f sends into y. The preimage of s is the set m t m is in s.
1 27 image of the empty set 2 15 parabola function g x x 2 3 14 example left as an exercise 3 49 the definition of the preimage of a set 5 11 disclaimer.
More generally evaluating a given function f at each element of a given subset a of its domain produces a set called the image of a under or through f similarly the inverse image or preimage of a given subset b of the codomain of f is the set of all elements of the domain that map to the members. Roughly speaking you might think of f x as a kind of distorted copy or image of x in b the preimage f 1 y of y is the set of all things in a that f sends into y. The preimage of s is the set m t m is in s. To decide if this function is onto we need to determine if every element in the codomain has a preimage in the domain.