\( g(x)=2 x+4 \) \( f(x)=x^{2}-4 x \) find \( (g, f)(x) \)

To find \( (g, f)(x) \), we are looking for the composition of the two functions, which means we will compute \( g(f(x)) \). First, we need to evaluate \( f(x) \): \( f(x) = x^{2} - 4x \). Now, substitute \( f(x) \) into \( g(x) \): \( g(f(x)) = g(x^{2} - 4x) = 2(x^{2} - 4x) + 4 \). Now simplify: \( = 2x^{2} - 8x + 4 \). So, \( (g, f)(x) = 2x^{2} - 8x + 4 \).