How do you find the domain of #ln(x^2-9)#?

1 Answer
Oct 2, 2016

Answer:

#x<-3, x>3#, #(x in RR)#

Explanation:

#lnx# is defined for all #x>0#

#:. ln(x^2-9)# is defined for #(x^2-9)>0#

#x^2>9#

#abs x> sqrt9 -> abs x >3#

Hence the domain of #ln(x^2-9)# is #x<-3, x>3#, #(x in RR)#

We can get a sense of this from the graph of #ln(x^2-9)# below:

graph{ln (x^2-9) [-12.66, 12.66, -6.32, 6.34]}