Given $f(x)=9 x$ and $g(x)=4 x^{2}+7$, find the following expressions. (a) $(f \circ g)(4)$ (b) $(g \circ f)(2)$ (c) (f $\circ f)(1)$ (d) $(g \circ g)(0)$

Step 1 ：Given the functions $f(x)=9x$ and $g(x)=4x^{2}+7$, we are asked to find the composition of these functions at certain points.

Step 2 ：For (a), we need to find $(f \circ g)(4)$, which means we substitute $g(4)$ into $f(x)$. First, we find $g(4) = 4(4)^{2}+7 = 71$. Then, we substitute this into $f(x)$ to get $f(g(4)) = 9(71) = 639$.

Step 3 ：For (b), we need to find $(g \circ f)(2)$, which means we substitute $f(2)$ into $g(x)$. First, we find $f(2) = 9(2) = 18$. Then, we substitute this into $g(x)$ to get $g(f(2)) = 4(18)^{2}+7 = 1303$.

Step 4 ：For (c), we need to find $(f \circ f)(1)$, which means we substitute $f(1)$ into $f(x)$. First, we find $f(1) = 9(1) = 9$. Then, we substitute this into $f(x)$ to get $f(f(1)) = 9(9) = 81$.

Step 5 ：For (d), we need to find $(g \circ g)(0)$, which means we substitute $g(0)$ into $g(x)$. First, we find $g(0) = 4(0)^{2}+7 = 7$. Then, we substitute this into $g(x)$ to get $g(g(0)) = 4(7)^{2}+7 = 203$.

Step 6 ：So, the final answers are: (a) $(f \circ g)(4) = \boxed{639}$, (b) $(g \circ f)(2) = \boxed{1303}$, (c) $(f \circ f)(1) = \boxed{81}$, and (d) $(g \circ g)(0) = \boxed{203}$.