Question

How do you find the domain of `f(x)=(x-3)/(x+4)`?

Answer 1

Domain is all real numbers except `x=-4`

Explanation:

The only limitation on the domain in this equation is undefined answers. Therefore, the limitation can be described by (denominator)=0 or in this case `x+4=0`, so `x` cannot equal `-4`.

Answer 2

`x inRR,x!=-4`

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+4=0rArrx=-4larrcolor(red)"excluded value"`

`"domain is "x inRR,x!=-4`

`x in(-oo,-4)uu(-4,+oo)larrcolor(blue)"in interval notation"`
graph{(x-3)/(x+4) [-10, 10, -5, 5]}