# Math Help - One to one

1. ## One to one

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.

2. 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.

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

4. 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'!