Question

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

Answer 1

Let the function fbe defined as,

f( x )={ ( ab,a+b ):a,b∈Z }

A relation from set Ato set Bis defined as function if every element in set Ahas a unique image in set B.

Consider an example,

( 1,4 )∈Z, ( 1×4,1+4 )∈Z ( 4,5 )∈Z

And

( −1,−4 )∈Z { ( −1×−4 ),( −1−4 ) }∈Z ( 4,−5 )∈Z

It can be observed that the first element 4has two images 5 and −5 in set B. Therefore, f is not a function.