(a) Let f(x): (-inf, 0) U (0 inf) --> R be defined by f(x) = x- (1/x) Show that f(x) has no inverse function. (b) Let g(x): (), inf) --> R be defined by gx) = x- (1/x) Show that g(x) has an inverse function.
I don't understand this. Please help!
If you graph y = x - 1/x, then it clearly fails the Horizontal Line Test over all real numbers, so f is not invertible. But if you restrict to positive real numbers, then it passes the Horizontal LIne Test, so g is invertible.