Question

What is the domain and range of `f(x) = 7/(x+3)`?

Answer 1

`x inRR,x!=-3,y inRR,y!=0`

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

`"domain is "x inRR,x!=-3`

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

`"let "y=7/(x+3)`

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

`y(x+3)=7`

`xy+3y=7`

`xy=7-3y`

`x=(7-3y)/ytoy!=0`

`"range is "y inRR,y!=0`

`(-oo,0)uu(0,oo)`
graph{7/(x+3) [-10, 10, -5, 5]}