Question

Find and simplify (f g)(x) where f(x)g(x) = -3x² / (x-3) = x³

Answer 1

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.