I am beginning abstract algebra and am having difficulty showing that some maps are bijective. It is a function f:V -> V where: f_1 : ( 1 -> 1 and a -> a) and... f_2 : ( 1 -> 1 and a -> a') where a and a' are the zeros of a polynomial. f_1 seems trivial. Whatever you plug in you get again so I can not see how it could not be bijective. Going back to my topology class it is the identity map I believe. I am having difficulties getting f_2 where a' is the algebraic conjugate. Does anyone have suggestions about how to think about it. I just can not seem to get past the first hurdle of where to start. Sorry for the formatting. I do not know how to make piecewise functions in tex. Thanks for any help in advance.