The problem asks to expand and simplify the expression $f(x) = (-3+x^{-3})(-4x^3+3)$.

1. Problem Description

The problem asks to expand and simplify the expression $f(x) = (-3+x^{-3})(-4x^3+3)$.

2. Solution Steps

We need to expand the product of the two binomials. We use the distributive property (also known as the FOIL method).

$f(x) = (-3+x^{-3})(-4x^3+3)$

$f(x) = (-3)(-4x^3) + (-3)(3) + (x^{-3})(-4x^3) + (x^{-3})(3)$

$f(x) = 12x^3 - 9 - 4x^{-3+3} + 3x^{-3}$

$f(x) = 12x^3 - 9 - 4x^0 + 3x^{-3}$

Since $x^0 = 1$, we have:

$f(x) = 12x^3 - 9 - 4 + 3x^{-3}$

$f(x) = 12x^3 - 13 + 3x^{-3}$

$f(x) = 12x^3 - 13 + \frac{3}{x^3}$

3. Final Answer

$f(x) = 12x^3 - 13 + \frac{3}{x^3}$