Let f be the subset of Z x Z defined by f = {(ab, a + b) : a, b ∈ Z}. Is f a function from Z to Z ?
Justify your answer

Solution:

The relation f is defined as

f = {(ab, a + b) : a, b ∈ Z

We know that a relation f from a set  A to a set B is said to be a function,

if every element of set A has unique images in set B.

Since,

2, 6, - 2, - 6 ∈ Z, (2 x 6, 2 + 6), (- 2 x - 6, - 2 + (- 6)) ∈ f i.e., (12, 8), (12, - 8) ∈ f

It can be seen that the same first element

i.e., 12 corresponds to two different images i.e., 8 and - 8.

Thus, relation f is not a function

NCERT Solutions Class 11 Maths Chapter 2 Exercise ME Question 11

Let f be the subset of Z x Z defined by f = {(ab, a + b) : a, b ∈ Z}. Is f a function from Z to Z ? Justify your answer

Summary:

A relation f be the subset of Z x Z defined by f = {(ab, a + b) : a, b ∈ Z}. We have found that relation f is not a function.