Final answer:
The value of (g\/f)(-4) is 41\/39, and the values not in the domain of g\/f are those that make the denominator zero, specifically x = 1\/3.
Step-by-step explanation:
The student's question involves two functions, g(x)=-3x^2+7 and f(x)=9x-3, and asks to find (a) the value of the composition (g\/f)(-4), and (b) the values not included in the domain of the quotient g\/f.
Part (a):
First, we evaluate f(-4) which gives us f(-4) = 9(-4) - 3 = -36 - 3 = -39.
Next, we evaluate g(-4) as g(-4) = -3(-4)^2 + 7 = -3(16) + 7 = -48 + 7 = -41.
Therefore, the value of (g\/f)(-4) is g(-4) \/ f(-4) = -41\/(-39) which simplifies to 41\/39 or approximately 1.0513.
Part (b):
The domain of the quotient g\/f consists of all real numbers except those that make the denominator, f(x), equal to zero. Finding where f(x) = 0, we set 9x - 3 = 0, which gives x = 1\/3. Thus, the domain of g\/f is all real numbers except x = 1\/3.