Domain of a function?

Question

What is the domain of y= LN(x^2-3x-4)

Answer 1

To find the domain of the function assigned, the natural log, you need to specify for which values of x, the function is well defined. We know that for logarithms in general, natural or in any base, we need the argument to be positive, i.e.,

 

x^2 - 3x - 4 > 0

 

Now all it takes is to solve the inequality just written. You should be able to check that this happens when 

x<-1 or x> 4. Hence

 

Domain is  {x<-1} ∪ {x>4}