Question

Find the domain of the function.

g(x) =x+5/x^2-36

Type answer in interval notation.

Answer 1

`Dom {g(x)} = (-\infty,+\infty)-\{-6, 6\}`

Explanation:

The domain of a domain of a function corresponds to the set of elements of
`x` so that
`g(x)` exists.

Let be
`g(x) = (x+5)/(x^(2)-36)`, 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
`x` so that denominator becomes zero.

Denominator is factorized to determined which values makes that function undefined:

`g(x) = (x+5)/((x+6)\cdot (x-6))`

Then, the domain of the function is represented by the following interval:

`Dom {g(x)} = (-\infty,+\infty)-\{-6, 6\}`