Question 427490
Solution:Since this is an rational function from its domain must rejected the values of x that make denominator zero. First factor the denominator:

{{{f(x)=(sqrt(x^2-16))/(x+4)(x+1))}}}

(x+4)(x+1)=0 => x+4=0 =>x=-4 and x+1=0 => x=-1 For this two values of x our function is undefined. Thus, its domain are the intervals:

  ( -infinity, -4), ( -4, -1 ), ( -1, +infinity ) or all real numbers different fro -4 and -1.