Find \( (f \circ g)(x) \) and \( (g \circ f)(x) \) and the domain of each.
\[
f(x)=x+3, g(x)=2 x^{2}-5 x-3
\]
\( (f \circ g)(x)=2 x^{2}-5 x-3 \) (Simplify your answer.)

Answer

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Answer

\( (f \circ g)(x) = 2x^2 - 5x \)

Steps

Step 1 ：\( (f \circ g)(x) = f(g(x)) \)

Step 2 ：\( f(g(x)) = (2x^2 - 5x - 3) + 3 \)

Step 3 ：\( (f \circ g)(x) = 2x^2 - 5x \)