a. Let f be a function, f : S S T. If there exists a function g: T S S such that g + f =
Chapter 5, Problem 50(choose chapter or problem)
a. Let f be a function, f : S S T. If there exists a function g: T S S such that g + f = iS, then g is called a left inverse of f. Show that f has a left inverse if and only if f is one-to-one. b. Let f be a function, f : S S T. If there exists a function g: T S S such that f + g = iT , then g is called a right inverse of f. Show that f has a right inverse if and only if f is onto. c. Let f: N S N be given by f(x) = 3x. Then f is one-to-one. Find two different left inverse functions for f. d. Let f: N+ S N+ be given by f(x) = l x 2 m . Then f is onto. Find two different right inverse functions for f
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