Question

How do you find the domain and range of `g(x)=8/(8-3x)`?

Answer 1

`x inRR,x!=8/3`
`y inRR,y!=0`

Explanation:

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

`"solve "8-3x=0rArrx=8/3larrcolor(red)"excluded value"`

`rArr"domain is "x inRR,x!=8/3`

`(-oo,8/3)uu(8/3,+oo)larrcolor(blue)"in interval notation"`

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

`y=8/(8-3x)`

`rArry(8-3x)=8`

`rArr8y-3xy=8`

`rArr-3xy=8-8y`

`rArrx=(8-8y)/(-3y)`

`"the denominator cannot equal zero"`

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

`rArr"range is "y inRR,y!=0`

`(-oo,0)uu(0,+oo)larrcolor(blue)"in interval notation"`
graph{8/(8-3x) [-10, 10, -5, 5]}