Given $f(x)=3 x^{2}-2$ and $g(x)=5-\frac{1}{2} x^{2}$, find the following expressions. (a) $(f \circ g)(4)$ (b) $(g \circ f)(2)$ (c) $(f \circ f)(1)$ (d) $(\mathrm{g} \circ \mathrm{g})(0)$ (a) $(f \circ g)(4)=25 \quad($ Simplify your answer.) (b) $(g \circ f)(2)=\square$ (Simplify your answer.)

Step 1 ：First, we find \(g(4) = 5 - \frac{1}{2} * 4^{2} = 5 - 8 = -3\).

Step 2 ：Then, we find \(f(-3) = 3 * (-3)^{2} - 2 = 3 * 9 - 2 = 27 - 2 = 25\).

Step 3 ：So, \((f \circ g)(4) = \boxed{25}\).

Step 4 ：First, we find \(f(2) = 3 * 2^{2} - 2 = 3 * 4 - 2 = 12 - 2 = 10\).

Step 5 ：Then, we find \(g(10) = 5 - \frac{1}{2} * 10^{2} = 5 - 50 = -45\).

Step 6 ：So, \((g \circ f)(2) = \boxed{-45}\).

Step 7 ：First, we find \(f(1) = 3 * 1^{2} - 2 = 3 - 2 = 1\).

Step 8 ：Then, we find \(f(1) = 3 * 1^{2} - 2 = 3 - 2 = 1\).

Step 9 ：So, \((f \circ f)(1) = \boxed{1}\).

Step 10 ：First, we find \(g(0) = 5 - \frac{1}{2} * 0^{2} = 5\).

Step 11 ：Then, we find \(g(5) = 5 - \frac{1}{2} * 5^{2} = 5 - 12.5 = -7.5\).

Step 12 ：So, \((g \circ g)(0) = \boxed{-7.5}\).