Q. 114.0( 59 Votes )

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 :

Given: f = {(ab, a + b): a, b Є Z}

For value 2, 6, -2, -6 Є Z,


f = {(2 × 6, 2 + 6), (-2 × -6, -2 - 6), (2 × -6, 2 - 6), (-2 × 6, -2 + 6).


f = {(12, 8), (12, -8), (-12, -4), (-12, 4).


Here we observe that same first element i.e. 12 corresponds to two different images that is 8 and -8. Thus f is not a function.


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