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}

Given: a function f : X →R, f (x) = x³ + 1, where X = {–1, 0, 3, 9, 7}

To find: function, f as set of ordered pairs and range of f

Explanation: given f : X →R, f (x) = x³ + 1, where X = {–1, 0, 3, 9, 7}

This means f is a function such that the first elements of all the ordered pair belong to the set X = {–1, 0, 3, 9, 7}. So this is the domain.

Now 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 becomes

f (-1) = (-1)³ + 1 = -1 + 1 = 0, so ordered pair is (-1, 0)

When x = 0, f (x) = x³ + 1 becomes

f (0) = (0)³ + 1 = 0 + 1 = 1, so ordered pair is (0, 1)

When x = 3, f (x) = x³ + 1 becomes

f (3) = (3)³ + 1 = 27 + 1 = 28, so ordered pair is (3, 28)

When x = 9, f (x) = x³ + 1 becomes

f (9) = (9)³ + 1 = 729 + 1 = 730, so ordered pair is (9, 730)

When x = 7, f (x) = x³ + 1 becomes

f (7) = (7)³ + 1 = 343 + 1 = 344, so ordered pair is (7, 344)

So the given function as a set of ordered pairs is

f = {(-1, 0), (0, 1), (3, 28), (9, 730), (7, 344)}

And the range of f contains all the second elements of all the ordered pairs of f, so

Range of f = {0, 1, 28, 730, 344}