Question

How do you find the domain and range of `f(x) = (x-2)/(x+1)`?

Answer 1

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

Explanation:

The denominator of f(x) cannot be zero as tis 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 is "x inRR,x!=-1`

`(-oo,-1)uu(-1,+oo)larrcolor(blue)"in interval notation"`

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

`f(x)=(x/x-2/x)/(x/x+1/x)=(1-2/x)/(1+1/x)`

`"as "xto+-oo,f(x)to(1-0)/(1+0)`

`rArry=1larrcolor(red)"excluded value"`

`rArr"range is "y inRR,y!=1`

`(-oo,1)uu(1,+oo)larrcolor(blue)"in interval notation"`
graph{(x-2)/(x+1) [-10, 10, -5, 5]}