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

To find the value of \( (g \circ f)(-2) \), we first need to calculate \( f(-2) \). Using the definition of \( f(x) \): \[ f(x) = 2x^2 + 4x + 2 \] Substituting \( -2 \) into \( f \): \[ f(-2) = 2(-2)^2 + 4(-2) + 2 = 2(4) - 8 + 2 = 8 - 8 + 2 = 2 \] Now that we have \( f(-2) = 2 \), we can calculate \( g(f(-2)) \) or \( g(2) \) using the definition of \( g(x) \): \[ g(x) = 2x - 7 \] Substituting \( 2 \) into \( g \): \[ g(2) = 2(2) - 7 = 4 - 7 = -3 \] Thus, the value of \( (g \circ f)(-2) \) is: \[ \boxed{-3} \]