Given a function f:A→B, and C⊆A, the image of C under f is defined as f(C)={f(x)∣x∈C}. In words, f(C) is the set of all the images of the elements...Given a function f:A→B, and C⊆A, the image of C under f is defined as f(C)={f(x)∣x∈C}. In words, f(C) is the set of all the images of the elements of C. Given a function f:A→B, and D⊆B, the preimage D of under f is defined as f−1(D)={x∈A∣f(x)∈D}. Hence, f−1(D) is the set of elements in the domain whose images are in C.
One-to-one functions focus on the elements in the domain. We do not want any two of them sharing a common image. Onto functions focus on the codomain. We want to know if it contains elements not assoc...One-to-one functions focus on the elements in the domain. We do not want any two of them sharing a common image. Onto functions focus on the codomain. We want to know if it contains elements not associated with any element in the domain.
