Answer:
[tex]Dom {g(x)} = (-\infty,+\infty)-\{-6, 6\}[/tex]
Step-by-step explanation:
The domain of a domain of a function corresponds to the set of elements of [tex]x[/tex] so that [tex]g(x)[/tex] exists.
Let be [tex]g(x) = \frac{x+5}{x^{2}-36}[/tex], which is a rational function whose denominator and numerators are both polynomials. From Algebra we know that rational functions are continuous unless such values of [tex]x[/tex] so that denominator becomes zero.
Denominator is factorized to determined which values makes that function undefined:
[tex]g(x) = \frac{x+5}{(x+6)\cdot (x-6)}[/tex]
Then, the domain of the function is represented by the following interval:
[tex]Dom {g(x)} = (-\infty,+\infty)-\{-6, 6\}[/tex]
