Find \( (f \circ g)(x) \) and \( (g \circ f)(x) \) and the domain of each.
\[
f(x)=x+17, g(x)=x-17
\]
\( (f \circ g)(x)=x \) (Simplify your answer.)
\( (g \circ f)(x)=x \) (Simplify your answer.)
The domain of \( (f \circ g)(x) \) is
(Type your answer in interval notation.)

Answer

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Answer

The domain of \( (f \circ g)(x) \) and \( (g \circ f)(x) \) is \( (-\infty, \infty) \)

Steps

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

Step 2 ：\( (f \circ g)(x) = f(x-17) = (x-17)+17 \)

Step 3 ：\( (f \circ g)(x) = x \)

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

Step 5 ：\( (g \circ f)(x) = g(x+17) = (x+17)-17 \)

Step 6 ：\( (g \circ f)(x) = x \)

Step 7 ：The domain of \( (f \circ g)(x) \) and \( (g \circ f)(x) \) is \( (-\infty, \infty) \)