## MCS013 - Assignment 8(d)

A function is

**if and only if for every in the codomain, there is an in the domain such that .***onto*So in the example you give, , the domain and codomain are the same set: Since, for every real number there is an such that , the function is onto. The example you include shows an explicit way to determine which maps to a particular , by solving for in terms of That way, we can pick any , solve for , and know the value of which the original function maps to that .

Side note:

Note that when we swap variables. We are guaranteed that every function that is onto and one-to-one has an inverse , a function such that .

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