If f(x)=2−x12 and g(x)=x2−9, what is the domain of g(x)÷f(x)?

1) f(x) = 2 - x^12

2) g(x) = x^2 - 9

3)

                   g(x)        2 - x^12
g(x)÷f(x) = = 
                   f(x)          x^2 - 9

The domain of g(x)÷f(x) is all the x values where the function is defined.

 It is defined for all x where the denominator is different of zero.

So, find where x^2 - 9 = 0.

That is x = 3 and x = -3.

And the domain is all the real numbers except x = 3 and x = -3.