For the given functions, find \( (f \circ g)(x) \) and \( (g \circ f)(x) \) and the domain of each.
\[
f(x)=\frac{6^{-}}{1-7 x}, g(x)=\frac{1}{x}
\]
\( (f \circ g)(x)=\frac{6 x}{x-7} \) (Simplify your answer.)
\( (g \circ f)(x)=\square \) (Simplify your answer.)

Answer

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Answer

\( (g \circ f)(x) = \frac{1 - 7x}{6} \)

Steps

Step 1 ：\( (f \circ g)(x) = f(g(x)) = \frac{6}{1 - 7(\frac{1}{x})} \)

Step 2 ：\( (f \circ g)(x) = \frac{6}{1 - \frac{7}{x}} \)

Step 3 ：\( (f \circ g)(x) = \frac{6x}{x - 7} \)

Step 4 ：\( (g \circ f)(x) = g(f(x)) = \frac{1}{\frac{6}{1 - 7x}} \)

Step 5 ：\( (g \circ f)(x) = \frac{1 - 7x}{6} \)