This question is from the book Abstract Algebra: Theory and Applications by Thomas W. Judson.
Chapter 1 – Question 23
Define a function on the real numbers by
$$f(x) = \frac{x + 1}{x – 1}.$$ What are the domain and range of $f$? What is the inverse of $f$? Compute $f \circ f^{-1}$ and $f^{-1} \circ f$.