Functions:Bijective

A function is bijective if it is both injective and surjective. That is, a bijective function maps each element of the domain to a distinct element in the codomain, and every element in the codomain is mapped to by exactly one element of the domain.

Injective, Surjective, and Bijective arrow diagrams

Examples of bijective functions:

• $f:A\to B,A=\{a,b,c\},B=\{1,2,3\}$ such that $f(a)=1$, $f(b)=2$, and $f(c)=3$
• $f:\mathbb {R} \to \mathbb {R} ,f(x)=3x+5$
• $f:\mathbb {R} \to \mathbb {R} ,f(x)=x^{3}$

Resources

• Course Textbook, pages 154-164