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.

Question

Philoid · Accepted 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.