Given $f(x)=3x^2-2$ 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) $(f\circ g)(4)=25($ Simplify your answer.)
(b) $(g\circ f)(2)=◻$ (Simplify your answer.)

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

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

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

Step 4 ：First, we find $f(2)=3\ast 2^2-2=3\ast 4-2=12-2=10$.

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

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

Step 7 ：First, we find $f(1)=3\ast 1^2-2=3-2=1$.

Step 8 ：Then, we find $f(1)=3\ast 1^2-2=3-2=1$.

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

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

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

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