Question

How do you find the domain of `f(x) = (x+9)/(x^2-361)`?

Answer 1

The domain is `x in (-oo,-19)uu(-19,19)uu(19,+oo)`

Explanation:

The denominator must be `!=0`

Therefore,

`x^2-361!=0`

`x^2!=361`

`x!=sqrt(361)`

`x!=19` and `x!=-19`

The domain is `x in (-oo,-19)uu(-19,19)uu(19,+oo)`

graph{(x+9)/(x^2-361) [-36.53, 36.52, -18.28, 18.27]}

Answer 2

`x inRR,x!=+-19`

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 values that x cannot be.

`"solve "x^2-361=0rArrx=+-19larrcolor(red)"excluded values"`

`"domain "x inRR,x!=+-19`

`"this can be expressed in "color(blue)"interval notation"`

`x in(-oo,-19)uu(-19,19)uu(19,oo)`
graph{(x+9)/(x^2-361) [-40, 40, -20, 20]}