Let A be a nonempty set and let f: A-->B be a function. Prove that f is one-to-one iff there exists a function g: B-->A such that gof = 1(subA). Can someone please show me how this is solved.

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Originally Posted by hayter221 Let A be a nonempty set and let f: A-->B be a function. Prove that f is one-to-one iff there exists a function g: B-->A such that gof = 1(subA). There is a well known theorem: There is an injection from A to B iff there is a surjection from B to A.

Are you sure, I thought it had something to do with inverses.

Originally Posted by hayter221 Are you sure, I thought it had something to do with inverses. Do you understand this problem? What I posted is all about 'inverses'!