Question

What is the domain of
(fg)(x)
f(x)=x2–4
g(x)=3x2

answer choices are
0
all real numbers except -2 and 2
all real numbers except 0
-2 and 2
all real numbers

Answer 1

does anybody know the answer

Answer 2

I will read that as
(f (g(x) )
= f(3x^2)
= (3x^2)^2 - 4
= 9x^4 - 4

Clearly the domain is the set of reals

We could have seen that without actually doing any work
Since no division took place, (worry about dividing by zero),
and no operations such as square roots were found, it was
obvious that we would get results no matter what x's we used.

Answer 3

or, if (fg)(x) = f(x)*g(x) the same logic applies. It's still just a polynomial, and the domain is all real numbers.