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Find the domain of the function.

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

Type answer in interval notation.

User Kellyb
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1 Answer

4 votes

Answer:


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\}

User PatrickSCLin
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