The function $f(x) = \frac{6}{7+x}$ is one-to-one.
(a) Find its inverse and check your answer. (b) Find the domain and the range of $f$ and $f^{-1}$.
(a) $f^{-1}(x) = $ (Simplify your answer.)
(b) Find the domain of $f$. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The domain is {$x|x \le $}.
(Type integers or fractions. Use a comma to separate answers as needed.)
B. The domain is {$x|x \ne $}.
(Type integers or fractions. Use a comma to separate answers as needed.)
C. The domain is {$x|x \ge $}.
(Type integers or fractions. Use a comma to separate answers as needed.)
D. The domain is the set of all real numbers.
Find the range of $f$. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The range is {$y|y \ge $}.
(Type integers or fractions. Use a comma to separate answers as needed.)
B. The range is {$y|y \le $}.
(Type integers or fractions. Use a comma to separate answers as needed.)
C. The range is {$y|y \ne $}.
(Type integers or fractions. Use a comma to separate answers as needed.)
D. The range is the set of all real numbers.