Q. 8 C5.0( 2 Votes )

Let A = [–1, 1], Then, discuss whether the following functions from A to itself are one – one, onto or bijective:

h(x) = x2

Answer :

TIP: One – One Function: – A function is said to be a one – one functions or an injection if different elements of A have different images in B.


So, is One – One function


a≠b


f(a)≠f(b) for all


f(a) = f(b)


a = b for all


Onto Function: – A function is said to be a onto function or surjection if every element of A i.e, if f(A) = B or range of f is the co – domain of f.


So, is Surjection iff for each , there exists such that f(a) = b


Bijection Function: – A function is said to be a bijection function if it is one – one as well as onto function.


Now, here f : A A : A = [–1, 1] given by function is h(x) = x2


Check for Injectivity:


Let x, y be elements belongs to A i.e. such that


h(x) = h(y)


x2 = y2


±x = ±y


Since it has many elements of A co – domain


Hence, h is not One – One function


Check for Surjectivity:


Let y be element belongs to A i.e. be arbitrary, then


h(x) = y


x2 = y


x = ±√y


Since h have no pre–image in domain A.


Hence, h is not onto function


Thus, It is not Bijective function


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Functions - 01Functions - 01Functions - 0152 mins
Functions - 10Functions - 10Functions - 1047 mins
Functions - 05Functions - 05Functions - 0558 mins
Functions - 07Functions - 07Functions - 0748 mins
Functions - 02Functions - 02Functions - 0253 mins
Functions - 03Functions - 03Functions - 0361 mins
Functions - 08Functions - 08Functions - 0840 mins
Functions - 12Functions - 12Functions - 1252 mins
Functions - 04Functions - 04Functions - 0460 mins
Functions - 09Functions - 09Functions - 0947 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses