Express the following functions
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:

According to the question,

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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