Question

How do you find the domain and range of `f(x)= (x+7)/(2x-8)`?

Answer 1

`x inRR,x!=4,y inRR,y!=1/2`

Explanation:

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

`"solve "2x-8=0rArrx=4larrcolor(red)"excluded value"`

`"domain is "x inRR,x!=4`

`(-oo,4)uu(4,+oo)larrcolor(blue)"in interval notation"`

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

`"let "y=(x+7)/(2x-8)`

`y(2x-8)=x+7`

`2xy-8y=x+7`

`2xy-x=7+8y`

`x(2y-1)=7+8y`

`x=(7+8y)/(2y-1)`

`"solve "2y-1=0rArry=1/2larrcolor(red)"excluded value"`

`"range is "y inRR,y!=1/2`

`(-oo,1/2)uu(1/2,+oo)`
graph{(x+7)/(2x-8) [-10, 10, -5, 5]}