Q. 125.0( 2 Votes )

Give examples of two functions f: N Z and g: Z Z such that gof is injective, but g is not injective.

Answer :

Define f: N Z as f(x) = x and g: N N as g(x)=|x|.


We first show that g is not injective.


It can be observed that:


g(– 1)=| – 1| = 1


g(1) =|1| = 1


Therefore, g(– 1) = g(1), but —1 1.


Therefore, g is not injective.


Now, gof: N Z is defined as gof(x) = g(f(x)) =g(x)=|x|.


Let x, y N such that gof(x) = gof(y).


|x|=|y|


Since x and y N both are positive.


|x|=|y| x=y


Hence, gof is injective


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
Some standard real functionsSome standard real functionsSome standard real functions61 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