Question

How do you find the domain of `f(x)=(3x-1)/(x^2+9)`?

Answer 1

The domain of `f(x)` is `RR`

Explanation:

The function is

`f(x)=(3x-1)/(x^2+9)`

`AA x in RR," the denominator is " x^2+9>0` and is `!=0`

Therefore,

The domain of `f(x)` is `RR` or in interval notation `x in (-oo, +oo)`

graph{(3x-1)/(x^2+9) [-7.02, 7.03, -3.51, 3.51]}

Answer 2

`x in(-oo,oo)`

Explanation:

`"the denominator of "f(x)" cannot be zero as this would"`
`"make "f(x)" undefined"`

`x^2+9" is always positive for all "x inRR`

`rArr"domain "x in(-oo,oo)`
graph{(3x-1)/(x^2+9) [-10, 10, -5, 5]}