Question

What is the domain and range of `y= -x/(x^2-1)`?

Answer 1

`x inRR,x!=+-1`
`y inRR,y!=0`

Explanation:

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

`"solve "x^2-1=0rArr(x-1)(x+1)=0`

`rArrx=+-1larrcolor(red)"excluded values"`

`"domain is "x inRR,x!=+-1`

`"divide terms on numerator/denominator by "x^2`

`y=(x/x^2)/(x^2/x^2-1/x^2)=(1/x)/(1-1/x^2)`

`"as "xto+-oo,yto0/(1-0)`

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

`"range is "y inRR,y!=0`
graph{-x/(x^2-1) [-10, 10, -5, 5]}