Question

What is the domain and range for `f(x) = - ( 1 / ( x + 1) )`?

Answer 1

`x in(-oo,-1)uu(-1,oo)`
`y in(-oo,0)uu(0,oo)`

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 "x+1=0rArrx=-1larrcolor(red)"excluded value"`

`"domain "x in(-oo,-1)uu(-1,oo)`

`"for the range rearrange making x the subject"`

`y=-1/(x+1)`

`y(x+1)=-1`

`xy+y=-1`

`xy=-1-y`

`x=-(1+y)/y`

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

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