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

Answer

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Answer

\( (g \circ f)(x) = 2x^2 - 3x - 12 \)

Steps

Step 1 ：\( (f \circ g)(x) = f(g(x)) = f(2x^2 - 7x - 4) \)

Step 2 ：\( (f \circ g)(x) = (2x^2 - 7x - 4) + 4 \)

Step 3 ：\( (f \circ g)(x) = 2x^2 - 7x \)

Step 4 ：\( (g \circ f)(x) = g(f(x)) = g(x+4) \)

Step 5 ：\( (g \circ f)(x) = 2(x+4)^2 - 7(x+4) - 4 \)

Step 6 ：\( (g \circ f)(x) = 2x^2 - 3x - 12 \)