Question

How do you find the domain of `f(x)=(x^2-9)/sqrt(x^2-4)`?

Answer 1

`(-oo,-2)uu(2,+oo)`

Explanation:

`x^2-9" is defined for all real values of x"`

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

`rArrx^2-4!=0`

`rArr(x-2)(x+2)!=0`

`rArrx!=+-2`

`"also "x^2-4>0`

`rArrx<-2,x>2`

`"domain is "(-oo,-2)uu(2,+oo)`

graph{(x^2-9)/(sqrt(x^2-4)) [-10, 10, -5, 5]}