Question

What is the domain of the function f(x)= ln(x^2-4)? Please show your work.

Answer 1

Hello,

A ln must have like argument a positive number.

x²-4>0 whose roots are 2 and -2.
To be positive,  the value of must be exterior of the roots


so -infinity<x<-2 or 2<x<infinity

Dom f(x)=IR - [-2; 2].

Answer 2

F(x) = ㏑(x² - 4)

Domain: {-2 ≤ x ≤ 2}, or [-2, 2]