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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PREVIOUSLet A = {1,2,3,4}, B = {1,5,9,11,15,16} and f = {(1,5), (2,9), (3,1), (4,5), (2,11)}Are the following true?(i) f is a relation from A to B(ii) f is a function from A to B.Justify your answer in each case.NEXTLet A = {9,10,11,12,13} and let f : A → N be defined by f(n) = the highest prime factor of n. Find the range of f.

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