Question

The function g is defined below . g(x) = (x - 5)/(x ^ 2 - 36) Find all values of x that are NOT in the domain of g. If there is more than one value, separate them with commas.

Answer 1

-6, 6

Explanation:

So we have the rational function:

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

The domain of a rational function is all real numbers except for when x is a zero of the denominator.

Thus, to determine the domain restrictions, set the denominator to 0 and solve for x:

`x^2-36=0`

Add 36 to both sides:

`x^2=36`

Take the square root of both sides:

`x=\pm 6`

So, the values that are not in the domain of g is: -6, 6.

And we're done!