If $$g(x)=3x^{2}+2x-3, f(0)=-3$$ and $$4g(f(x))=3x^{2}-32x+72$$, then f(g(2)) is equal to:

We need to find $$f(g(2))$$ given $$g(x) = 3x^2 + 2x - 3$$, $$f(0) = -3$$, and $$4g(f(x)) = 3x^2 - 32x + 72$$.

First, we determine the form of $$f(x)$$ from the relation between $$f$$ and $$g$$. Since $$4g(f(x)) = 4[3(f(x))^2 + 2f(x) - 3] = 12(f(x))^2 + 8f(x) - 12 = 3x^2 - 32x + 72$$, we assume $$f(x) = px + q$$. The condition $$f(0) = q = -3$$ then gives $$f(x) = px - 3$$.

Substituting into the equation yields
$$12(px-3)^2 + 8(px-3) - 12 = 3x^2 - 32x + 72$$
$$12(p^2x^2 - 6px + 9) + 8px - 24 - 12 = 3x^2 - 32x + 72$$
$$12p^2x^2 - 72px + 108 + 8px - 36 = 3x^2 - 32x + 72$$
$$12p^2x^2 + (-72p + 8p)x + 72 = 3x^2 - 32x + 72$$
$$12p^2x^2 - 64px + 72 = 3x^2 - 32x + 72$$.

Comparing coefficients of like powers of $$x$$ gives
$$12p^2 = 3 \implies p^2 = 1/4 \implies p = \pm 1/2$$
$$-64p = -32 \implies p = 1/2$$.

Hence, $$f(x) = \frac{x}{2} - 3$$.

Next, we compute
$$g(2) = 3(4) + 2(2) - 3 = 12 + 4 - 3 = 13$$.

Finally, we evaluate
$$f(g(2)) = f(13) = \frac{13}{2} - 3 = \frac{13 - 6}{2} = \frac{7}{2}$$.

Therefore, the value of $$f(g(2))$$ is $$\frac{7}{2}$$.