consider 2 functions , the function from to that is denoted as where for all , is called the composite function of over .
an equivalent definition from gallian's:
let and . the composition is the mapping from to defined by for all in .
and arent necessarily equal
associativity if then this equality holds true:
are functions therefore is a function are functions therefore is a function therefore and are functions and their domain and range are equal let , then:
let be functions:
- if are surjective, then is surjective
- if are injective, then is injective
- if are total, then is total
being surjective or injective doesnt necessarily mean or are too