Question

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 ?

Answer 1

`f(-3) = (3 * (-3) - 6) / (-3) + 4.5 = (-9 - 6) / (-3) = -15 / (-3) = 5`

`f(-1) = (3 * (-1) - 6) / (-3) + 4.5 = (-3 - 6) / (-1) = -9 / (-3) = 3`

`f(2) = (3 * 2 - 6) / 2 + 4.5 = (6 - 6) / 2 = 0 / 2 = 0`

`f(4) = (3 * 4 - 6) / 4 + 4.5 = (12 - 6) / 4 = 6 / 4 = 1(1)/(2) = 1.5`

`f(5) = (3 * 5 - 6) / 5 + 4.5 = (15 - 6) / 5 = 9 / 5 = 1(4)/(5) = 1.8`

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

Answer 2

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

Explanation:

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

To find : The range of the function ?

Solution :

Function
`f(x)=(3x-6)/(x)+4.5`

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,

`f(-3)=(3(-3)-6)/(-3)+4.5`

`f(-3)=(-15)/(-3)+4.5`

`f(-3)=5+4.5`

`f(-3)=9.5`

Put x=-1,

`f(-1)=(3(-1)-6)/(-3)+4.5`

`f(-1)=(-9)/(-3)+4.5`

`f(-1)=3+4.5`

`f(-1)=7.5`

Put x=2,

`f(2)=(3(2)-6)/(-3)+4.5`

`f(2)=(0)/(-3)+4.5`

`f(2)=0+4.5`

`f(2)=4.5`

Put x=4,

`f(4)=(3(4)-6)/(-3)+4.5`

`f(4)=(6)/(-3)+4.5`

`f(4)=-2+4.5`

`f(4)=2.5`

Put x=5,

`f(5)=(3(5)-6)/(-3)+4.5`

`f(5)=(9)/(-3)+4.5`

`f(5)=-3+4.5`

`f(5)=1.5`

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