Gw mau tau Images and preimages dari Fungsi (matematika). Jelasin dalam bahasa sunda

The image of an element x∈X under f is the output f(x).

The image of a subset A⊂X under f is the subset of Y defined by

f(A) := {f(x) : x in A}.

Notice that the range of f is the image f(X) of its domain. In our function above, the image of {2,3} under f is f({2, 3}) = {c, d} and the range of f is {a, c, d}.

Note that with this definiton, the direct image f becomes a function whose domain is the set of all subsets of X (also known as the power set of X) and whose codomain is the power set of Y. Note that the same notation is used for the original function f and 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

f −1(B) := {x in X : f(x)∈B}.

In our function above, the preimage of {a, b} is f −1({a, b}) = {1}.

Note that with this definiton, f −1 becomes a function whose domain is the power set of Y and whose codomain is the power set of X.

Some consequences that follow immediately from these definitions are:

f(A1 ∪ A2) = f(A1) ∪ f(A2).

f(A1 ∩ A2) ⊆ f(A1) ∩ f(A2).

f −1(B1 ∪ B2) = f −1(B1) ∪ f −1(B2).

f −1(B1 ∩ B2) = f −1(B1) ∩ f −1(B2).