For the pair of functions, find the indicated composition. a) Given functions \( f(x)=4 x^{2}+3 x+5 \) and \( g(x)=3 x-3 \). Find \( (g \circ f)(x) \).

To find \( (g \circ f)(x) \), we first apply the function \( f(x) \) and then use the result as the input for \( g(x) \). First, we have: \[ f(x) = 4x^2 + 3x + 5 \] Now, we substitute \( f(x) \) into \( g(x) \): \[ g(f(x)) = g(4x^2 + 3x + 5) \] Using the definition of \( g(x) = 3x - 3 \): \[ g(4x^2 + 3x + 5) = 3(4x^2 + 3x + 5) - 3 \] Now we can distribute and simplify: \[ g(4x^2 + 3x + 5) = 12x^2 + 9x + 15 - 3 = 12x^2 + 9x + 12 \] Thus, the composition \( (g \circ f)(x) \) is: \[ \boxed{12x^2 + 9x + 12} \]