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I.e - from knowing the function you can determine the co-domain - e.g - if it is specified that real functions are going in, and for something simple like 2x + 1 = f(x) - then surely from this you can deduce the co-domain will also be all reals.

- also say if the co-domain and function have both been specified, then given either the domain/range - surely you are able to deduce domain/range accordingly.

- E.g - x^1/2.

Am I correct in thinking that its inverse can only be formed if you either:

- restrict the domain

or

- restrict the codomain

I am pretty certain the 1st option holds, however for the 2nd is my defintion of co-domain correct?

Thanks alot if anyone will shed some light on this, greatly appreciated :).