(Solved): For the given functions, find \( (f \circ g)(x) \) and \( (g \circ f)(x) \) and the domain of each ...

For the given functions, find \( (f \circ g)(x) \) and \( (g \circ f)(x) \) and the domain of each. \[ f(x)=\frac{4}{1-7 x}, g(x)=\frac{1}{x} \] \( (f \circ g)(x)=\mid \quad \) (Simplify your answer.) \( (g \circ f)(x)=\quad( \) Simplify your answer. \( ) \) What is the domain of \( f \circ g \) ? A. \( (-\infty,-7) \cup(-7,0) \cup(0, \infty) \) B. \( (-\infty, 0) \cup(0,7) \cup(7, \infty) \) C. \( (-\infty, 7) \cup(7, \infty) \) D. \( (-\infty, 0) \cup(0, \infty) \) What is the domain of \( \mathrm{g} \circ \mathrm{f} \) ? A. \( \left(-\infty, \frac{1}{7}\right) \cup\left(\frac{1}{7}, \infty\right) \) B. \( (-\infty, 0) \cup(0, \infty) \) C. \( (-\infty, 7) \cup(7, \infty) \) D. \( (-\infty, 0) \cup\left(0, \frac{1}{7}\right) \cup\left(\frac{1}{7}, \infty\right) \)