Question

How do you find the domain and range of `1/(3t+12)`?

Answer 1

`"domain "(-oo,-4)uu(-4,oo)`
`"range "(-oo,0)uu(0,oo)`

Explanation:

`"let " y=1/(3t+12)`

`"the denominator cannot be zero as this would make y"`
`"undefined. Equating the denominator to zero and solving"`
`"gives the value that t cannot be"`

`"solve "3t+12=0rArrt=-4larrcolor(red)"excluded value"`

`rArr"domain "(-oo,-4)uu(-4,oo)`

`"rearrange making t the subject"`

`y(3t+12)=1`

`rArr3ty+12y=1`

`rArr3ty=1-12y`

`rArrt=(1-12y)/(3y)`

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

`rArr"range "(-oo,0)uu(0,oo)`
graph{1/(3x+12) [-10, 10, -5, 5]}