Q. 6 Give examples of two functions f : N \rightarrow Zand g : Z \rightarrow Z such that gofis
injective but g is not injective.

(Hint : Consider f (x) = x and g (x) = | x |).

Answers (1)

f : N \rightarrow Z

g : Z \rightarrow Z

f (x) = x

g (x) = | x |

One - one:

Since g (x) = | x |

  f(1)=\left | 1 \right | = 1

f(-1)=\left |- 1 \right | = 1

As we can see f(1)=f(-1)   but  1\neq -1 so  g(x)  is not one-one.

Thus , g(x) is not injective.

gof : N \rightarrow Z

gof(x) = g(f(x)) = g(x) =\left | x \right |

Let   gof(x)=gof(y)\, \, \, \, \, x,y \in N

                 \left | x \right |=\left | y \right |

       Since,  x,y \in N   so x and y are both positive.

        \therefore x=y

Hence, gof is injective.

 

 

 

      

 

 

 

Preparation Products

JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Rank Booster NEET 2021

This course will help student to be better prepared and study in the right direction for NEET..

₹ 13999/- ₹ 9999/-
Buy Now
Knockout JEE Main April 2021 (Easy Installments)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 4999/-
Buy Now
Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout NEET May 2022

An exhaustive E-learning program for the complete preparation of NEET..

₹ 34999/- ₹ 24999/-
Buy Now
Exams
Articles
Questions