Question

How do you find the domain and range for `y = (3(x-2))/x`?

Answer 1

Domain : `x < 0 " or" x > 0`

Range : -6 / (x - 3)#

Explanation:

The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

Find the domain and range of the function y = 1 x + 3 − 5 . To find the excluded value in the domain of the function, equate the denominator to zero and solve for .

The range of the function is same as the domain of the inverse function.

`y = (3(x - 2)) / x`

Domain : When x = 0, point x=0 is undefined.

The function domain `x < 0 " or " x > 0`

Range : Set of values of the dependent variable for which a function is defined.

Function range is the combined domain of the inverse functions.

`"inverse of " (3(x-2))/x : - 6/(x-3)`

graph{(3 (x - 2)) / x [-10, 10, -5, 5]}

Answer 2

`x inRR,x!=0,y inRR,y!=3`

Explanation:

The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be.

`x=0larrcolor(red)"excluded value"`

`"domain is "x inRR,x!=0`

`(-oo,0)uu(0,oo)larrcolor(blue)"in interval notation"`

`"to find the range, rearrange making x the subject"`

`xy=3x-6`

`xy=3x=-6`

`x(y-3)=-6`

`x=-6/(y-3)`

`"solve "y-3=0rArry=3larrcolor(red)"excluded value"`

`"range is "y inRR,y!=3`

`(-oo,3)uu(3,oo)`
graph{(3x-6)/x [-20, 20, -10, 10]}