Function : Not onto
Function : one-one and onto ( or bijective )
A function f : X → Y is said to be one-one and onto ( or bijective ), if f is both one-one and onto .
Numerical : Let A be the set of all 50 students of Class X in a school . Let f : A →N be function defined by f ( x ) = roll number of the student x . Show that f is one-one but not onto .
Solution : Every student in the class has unique roll number , so it is 1-1 .
Only roll number 1-50 is assigned to students . Other roll numbers 51 onwards are free & don ’ t point to any student , so it is not onto .
Composition of functions
Let f : A → B and g : B → C be two functions . Then the composition of f and g , denoted by gof , is defined as the function gof : A → C given by gof ( x ) = g ( f ( x )), ∀ x ∈ A .