Define by where denotes the set of all integers.

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Define

g: \mathbb Z \to \mathbb Z

g(n)=2n+3

where

\mathbb Z

denotes the set of all integers. (i) Write the set that represents the range of

g

. (ii) Is

g

an onto function? Prove your answer. (iii) Identify all integers

k

for which the equation

g(n)=k

has no solution in

\mathbb Z

, and justify why these

k

fail to have pre-images.