Question

Find the domain and range of the function F(x)=3+x/3-x?

Answer 1

`x inRR,x!=3,y inRR,y!=-1`

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

`rArr"domain "x inRR,x!=3`

`x in(-oo,3)uu(3,oo)larrcolor(blue)"in interval notation"`

`f(x)=(3+x)/(3-x)`

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

`f(x)=(3/x+x/x)/(3/x-x/x)=(3/x+1)/(3/x-1)`

`"as "xto+-oo,f(x)to(0+1)/(0-1)=-1larrcolor(red)"excluded value"`

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

`y in(-oo,-1)uu(-1,oo)`
graph{(3+x)/(3-x) [-10, 10, -5, 5]}