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Question
Express the following functions as set of ordered pairs and determine their range.
f : X → R, f(x) = x3 + 1, where X = {–1, 0, 3, 9, 7}
Solution
A function f: X →R, f (x) = x3 + 1
Where X = {–1, 0, 3, 9, 7}
Domain = f is a function such that the first elements of all the ordered pair belong to the set X = {–1, 0, 3, 9, 7}.
The second element of all the ordered pair are such that they satisfy the condition f(x) = x3 + 1
When x = – 1,
f(x) = x3 + 1
f(– 1) = (– 1)3 + 1
= – 1 + 1
= 0
⇒ Ordered pair = (–1, 0)
When x = 0,
f(x) = x3 + 1
f(0) = (0)3 + 1
= 0 + 1
= 1
⇒ Ordered pair = (0, 1)
When x = 3,
f(x) = x3 + 1
f(3) = (3)3 + 1
= 27 + 1
= 28
⇒ Ordered pair = (3, 28)
When x = 9,
f(x) = x3 + 1
f(9) = (9)3 + 1
= 729 + 1
= 730
⇒ Ordered pair = (9, 730)
When x = 7,
f(x) = x3 + 1
f(7) = (7)3 + 1
= 343 + 1
= 344
⇒ Ordered pair = (7, 344)
Therefore, the given function as a set of ordered pairs is
f = {(–1, 0), (0, 1), (3, 28), (7, 344), (9, 730)}
And,
Range of f = {0, 1, 28, 730, 344}
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