Given the definitions of \( f(x) \) and \( g(x) \) below, find the value of \( (g \circ f)(1) \) \[ \begin{aligned} f(x)=4 x-2 \\ g(x)=3 x^{2}+3 x-7\end{aligned} \]

To find the value of \( (g \circ f)(1) \), we need to first calculate \( f(1) \) and then substitute that result into \( g(x) \). 1. **Calculate \( f(1) \)**: \[ f(1) = 4(1) - 2 = 4 - 2 = 2 \] 2. **Now, use the result to find \( g(f(1)) = g(2) \)**: \[ g(2) = 3(2^2) + 3(2) - 7 \] \[ g(2) = 3(4) + 6 - 7 \] \[ g(2) = 12 + 6 - 7 = 11 \] Thus, the value of \( (g \circ f)(1) \) is \( \boxed{11} \).