Discrete Math - Functions

A special kind of relation f ⊆ A×B is called a function from set A to set B if every element in set A has only 1 image in set B. This can be denoted as: f:A→B. A real valued function is a function which states f:R→ R. In this case we can use arithmetic operators between functions.

An injective function has every image relating to distinct elements in x under f.

Figure 42

A surjective function says every element in y is the image of some element x under f.

Figure 43

There are non-surjective and non-injective functions.

Figure 44

A composition of functions states that given 2 functions f:A→B  and g:B→C, we define a composition as g∘f:A→C.

Invertible functions state that $ f^-1 :A→B $ can yield $ f^-1 :B→A $.


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