What's the domain of the function?

The domain of a function is the list of "x" values that are valid.

Since you have the product of two polynomials that, by themselves, have no limitations, the limitations come in when the denominator is zero.

x² - 36 = 0

x² = 36

x = ±6

So the domain is all real numbers except for -6 and 6.  In Interval notation this would be:

(-∞, -6) U (-6, 6) U (6, ∞)

               7x

g(x) = ------------

            x² - 36

You cannot have 0 in the denominator so

            x² - 36 ≠ 0   ⇒

            x² ≠ 36        ⇒

            x ≠ ±6

Therefore, the domain of g(x) is

           DOMAIN = all x such that x ≠ ±6,

           written as (-∞,-6) U (-6,6) U (6,+∞) ............ANS