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Question
Let A = {−2, −1, 0, 1, 2} and f : A → Z be a function defined by f(x) = x2 − 2x − 3. Find:
(a) range of f, i.e. f(A).
Solution
(a) Given:
f (x) = x2 − 2x − 3
f (−2) = (− 2)2 − 2(− 2) − 3
= 4 + 4 – 3
= 8 − 3 = 5
f (−1) = (−1)2 − 2(−1) − 3
= 1+ 2 − 3
= 3 − 3 = 0
f (0) = (0)2 − 2(0) − 3
= 0 − 0 − 3
= − 3
f (1) = (1)2 − 2(1) − 3
= 1 − 2 − 3
=1 − 5 = − 4
f (2) = (2)2 – 2(2) − 3
= 4 − 4 – 3
= 4 – 7 = − 3
Thus, range of f(A) = (− 4, − 3, 0, 5).
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