Step 1. We need to find out when g(x) does not exist or it becomes undefined. In this case, the denominator cannot equal to zero. So we need to find out when the denominator is equal to zero.
Step 2. Let's look at the denominator given as
Step 3. We recognize that this equation is a difference of squares so we can factor is as
and we set the function equal to zero. A zero will occur when x=6 and x=-6.
Step 4. So the domain is everywhere except at x=6 and x=-6. Use can inequalities to describe this as follows: -6 6.
I hope the above steps were helpful.
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