the domain of the function?

domain means values of x for which the function's value exists

for g(x) = 9x/(x^2 - 16),

g(x) exists whenever x^2 - 16 is not zero (because if it is zero, you'd have to divide by 0 to get g(x) which you cannot do)

x^2 - 16 = 0 for x = 4 and -4

so domain is all real numbers except 4 and -4

does this make sense ?

x^2 may not be 0

So the values in wich it is 0, can't be in the function

x^2=0

x*x=0

x=0

D(g)= R/0

Unless your function is 9x/(x^2-16) in that case

x^2-16=0

x^2=16

x=16^(1/2)

x=4 V x=-4

D(g)= R/{-4,4}

I am going to assume that x^2-16 is in the denominator.

A fraction is ALWAYS undefined when 0 is in the denominator so:

x^2-16 is not equal to 0. (I will use != for not equal to)

(x+4)(x-4) != 0

x != -4,4

Domain of the function is all real numbers excluding -4 and 4