Problem
Previous Problem Problem List Next Problem (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.
Solution
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) \(g(f(-3)) = \boxed{43}\)
