Q. 1 A3.8( 17 Votes )

Give an example of a function

Which is one – one but not onto.

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


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

Now, Let, given by f(x) = x2

Check for Injectivity:

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

So, from definition

f(x) = f(y)

x2 = y2

x2 – y2 = 0

(x – y)(x + y) = 0

As therefore x + y>0

x – y = 0

x = y

Hence f is One – One function

Check for Surjectivity:

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

f(x) = y

x2 = y

not belongs to N for non–perfect square value of y.

Therefore no non – perfect square value of y has a pre image in domain N.

Hence, given by f(x) = x2 is One – One but not onto.

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
Inverse Trigonometric Functions - 01Inverse Trigonometric Functions - 01Inverse Trigonometric Functions - 0161 mins
Range of FunctionsRange of FunctionsRange of Functions58 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
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
view all courses