Final answer:
To find (f g)(x), substitute the expression for f(x)g(x) into the function f g(x) = f(g(x)). Simplify the expression f(x)g(x) = -3x² / (x-3) = x³, and then substitute it into the function. Further simplify the expression by cubing the numerator and denominator separately if desired.
Step-by-step explanation:
To find (f g)(x), we need to substitute the expression for f(x)g(x) into the function f g(x) = f(g(x)).
First, let's simplify the expression f(x)g(x) = -3x² / (x-3) = x³:
-3x² / (x-3) = x³
Next, substitute the simplified expression into the function:
f g(x) = (-3x² / (x-3))³
We can leave the expression in this form, or we can further simplify by cubing the numerator and denominator separately.