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(1 point) Suppose that $f(x)=3 x^{2}-3 x+2$ and
\[
g(x)=\left\{\begin{array}{lr}
4 x-6 & x< 1 \\
-3 & 1 \leq x< 8 \\
x+5 & x \geq 8
\end{array}\right.
\]

Find the following:
(a) $(f \cdot g)(4)=-9 x^{\wedge} 2+9 x-2$
(b) $(g \cdot f)(-3)=$

Note: You can earn partial credit on this problem.

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Answer

Final Answer: \n(a) $f(g(4)) = \boxed{38}$ \n(b) $g(f(-3)) = \boxed{43}$

Steps

Step 1 ：Define the functions $f(x)$ and $g(x)$ as given in the problem.

Step 2 ：Calculate the value of $f(g(4))$.

Step 3 ：Calculate the value of $g(f(-3))$.

Step 4 ：The calculated values are 38 and 43 respectively.

Step 5 ：Final Answer: \n(a) $f(g(4)) = \boxed{38}$ \n(b) $g(f(-3)) = \boxed{43}$