Find $(f \circ g)(x)$ and $(g \circ f)(x)$ and the domain of each. \[ f(x)=x+4, g(x)=2 x^{2}-7 x-4 \] $(f \circ g)(x)=\square($ Simplify your answer.) The domain of $(f \circ g)(x)$ is $\square$. (Type your answer in interval notation.) $(g \circ f)(x)=\square($ Simplify your answer.) The domain of $(g \circ f)(x)$ is $\square$. (Type your answer in interval notation.)

Step 1 ：Define the functions \(f(x) = x + 4\) and \(g(x) = 2x^2 - 7x - 4\).

Step 2 ：Calculate the composition of the functions, \(f \circ g(x)\) and \(g \circ f(x)\).

Step 3 ：Simplify the results to get \(f \circ g(x) = 2x^2 - 7x\) and \(g \circ f(x) = 2x^2 + 9x - 4\).

Step 4 ：Determine the domain of each function. Since \(g(x)\) is a quadratic function and \(f(x)\) is a linear function, both are defined for all real numbers.

Step 5 ：\(\boxed{(f \circ g)(x) = 2x^2 - 7x}\), the domain of \((f \circ g)(x)\) is \(\boxed{(-\infty, \infty)}\), \(\boxed{(g \circ f)(x) = 2x^2 + 9x - 4}\), and the domain of \((g \circ f)(x)\) is \(\boxed{(-\infty, \infty)}\).