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}

Home » 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}

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:

Provided that,

A function $\mathrm{f}: \mathrm{X} \rightarrow \mathrm{R}, \mathrm{f}(\mathrm{x})=\mathrm{x}^{3}+1$ , in which $\mathrm{X}=\{-1,0,3,9,7\}$

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 $f (x) = x^{3} + 1$

When $x=-1$

$f(x)=x^{3}+1$

$f(-1)=(-1)^{3}+1=-1+1=0 \Rightarrow$ ordered pair $=(-1,0)$

When $x=0$

$f(x)=x^{3}+1$

$f(0)=(0)^{3}+1=0+1=1 \Rightarrow$ ordered pair $=(0,1)$

When $x=3$

$f(x)=x^{3}+1$

$f(3)=(3)^{3}+1=27+1=28 \Rightarrow$ ordered pair $=(3,28)$

When $x=9$

$f(x)=x^{3}+1$

$f(9)=(9)^{3}+1=729+1=730 \Rightarrow$ ordered pair $=(9,730)$

When $x=7$

$f(x)=x^{3}+1$

$f(7)=(7)^{3}+1=343+1=344 \Rightarrow$ ordered pair $=(7,344)$

As a result, the provided 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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