Certainly! Let's solve this question step by step:

Given function: \(g(x) = x^2 + 3x + 4\)

We want to find \(g(x + 1) - g(x)\).

First, let's find \(g(x + 1)\):

\[g(x + 1) = (x + 1)^2 + 3(x + 1) + 4\]

\[= x^2 + 2x + 1 + 3x + 3 + 4\]

\[= x^2 + 5x + 8\]

Now, subtract \(g(x)\) from \(g(x + 1)\) to find \(g(x + 1) - g(x)\):

\[g(x + 1) - g(x) = (x^2 + 5x + 8) - (x^2 + 3x + 4)\]

\[= x^2 + 5x + 8 - x^2 - 3x - 4\]

\[= 2x + 4\]