Use $f(x)=5 x-3$ and $g(x)=2-x^{2}$ to evaluate the expression. (a) $(f \circ f)(x)$ (b) $(g \circ g)(x)$

Step 1 ：Given the functions $f(x)=5x-3$ and $g(x)=2-x^{2}$, we are asked to evaluate the expressions $(f \circ f)(x)$ and $(g \circ g)(x)$.

Step 2 ：The composition of two functions, $f$ and $g$, denoted as $(f \circ g)(x)$, is defined as $f(g(x))$.

Step 3 ：For part (a), we need to find $(f \circ f)(x)$, which means we need to substitute $f(x)$ into itself. So, $(f \circ f)(x) = f(f(x)) = f(5x-3) = 5(5x-3) - 3 = 25x - 15 - 3 = 25x - 18$.

Step 4 ：For part (b), we need to find $(g \circ g)(x)$, which means we need to substitute $g(x)$ into itself. So, $(g \circ g)(x) = g(g(x)) = g(2-x^{2}) = 2 - (2-x^{2})^{2}$.

Step 5 ：Final Answer: (a) $(f \circ f)(x) = \boxed{25x - 18}$, (b) $(g \circ g)(x) = \boxed{2 - (2 - x^2)^2}$