Question

How do you find the domain of `g(x) = x/(x^2+4)` using set-builder notation and interval notation?

Answer 1

`(-oo,+oo)`

Explanation:

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

`"solve "x^2+4=0rArrx^2=-4`

`"this has no real solutions "`

`rArrx^2+4!=0`

`"domain is "{x:x inRR}larrcolor(blue)"set-builder notation"`

`"or "(-oo,+oo)larrcolor(blue)"interval notation"`
graph{x/(x^2+4) [-10, 10, -5, 5]}