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The domain of the function f(x)= (3x-6)/(x)+4.5 is {-3,-1,2,4,5} the range for the given f(x)= (3x-6)/(x)+4.5 is ?

Respuesta :

Seprum
[tex]f(-3) = (3 * (-3) - 6) / (-3) + 4.5 = (-9 - 6) / (-3) = -15 / (-3) = 5[/tex]
[tex]f(-1) = (3 * (-1) - 6) / (-3) + 4.5 = (-3 - 6) / (-1) = -9 / (-3) = 3 [/tex]
[tex]f(2) = (3 * 2 - 6) / 2 + 4.5 = (6 - 6) / 2 = 0 / 2 = 0 [/tex]
[tex]f(4) = (3 * 4 - 6) / 4 + 4.5 = (12 - 6) / 4 = 6 / 4 = 1\frac{1}{2} = 1.5 [/tex]
[tex]f(5) = (3 * 5 - 6) / 5 + 4.5 = (15 - 6) / 5 = 9 / 5 = 1\frac{4}{5} = 1.8 [/tex]

So the range is {5, 3, 0, 1.5, 1.8}

Answer:

The range of the function is {9.5,7.5,4.5,2.5,1.5}.

Step-by-step explanation:

Given : The domain of the function [tex]f(x)=\frac{3x-6}{x}+4.5[/tex] is {-3,-1,2,4,5}.

To find : The range of the function ?

Solution :

Function [tex]f(x)=\frac{3x-6}{x}+4.5[/tex]

Domain of the function {-3,-1,2,4,5}.

Range is defined as the set of values that corresponds with the domain.

To find the range we put all values of x to get f(x),

Put x=-3,

[tex]f(-3)=\frac{3(-3)-6}{-3}+4.5[/tex]

[tex]f(-3)=\frac{-15}{-3}+4.5[/tex]

[tex]f(-3)=5+4.5[/tex]

[tex]f(-3)=9.5[/tex]

Put x=-1,

[tex]f(-1)=\frac{3(-1)-6}{-3}+4.5[/tex]

[tex]f(-1)=\frac{-9}{-3}+4.5[/tex]

[tex]f(-1)=3+4.5[/tex]

[tex]f(-1)=7.5[/tex]

Put x=2,

[tex]f(2)=\frac{3(2)-6}{-3}+4.5[/tex]

[tex]f(2)=\frac{0}{-3}+4.5[/tex]

[tex]f(2)=0+4.5[/tex]

[tex]f(2)=4.5[/tex]

Put x=4,

[tex]f(4)=\frac{3(4)-6}{-3}+4.5[/tex]

[tex]f(4)=\frac{6}{-3}+4.5[/tex]

[tex]f(4)=-2+4.5[/tex]

[tex]f(4)=2.5[/tex]

Put x=5,

[tex]f(5)=\frac{3(5)-6}{-3}+4.5[/tex]

[tex]f(5)=\frac{9}{-3}+4.5[/tex]

[tex]f(5)=-3+4.5[/tex]

[tex]f(5)=1.5[/tex]

Therefore, The range of the function is {9.5,7.5,4.5,2.5,1.5}.

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