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

##### 1 Answer

Jan 20, 2018

#### 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]}