<p>Prove that if f and g are 1-1 then<img src=\"https://s3.amazonaws.com/answer-

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<p>Prove that if f and g are 1-1 then<img src="https://s3.amazonaws.com/answer-board-image/cramster-equation-20101122105134634260198948150868764.gif" alt="" align="absMiddle" />is 1-1.&#160;</p> Prove that if f and g are 1-1 then

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given that f : A --> B and g: B--> C are one one functions. i.e. for every f(x) = f(y) in B, there corresponds x=y in A. also, considering the range f as the part of the domain for g, g: B--> C is a one one function. so, g(p) = g(q) in C means p = q in B. comparing p = q with f(x) = f(y) , we can say that (gof)(x) = (gof)(y) ==> g(f(x)) =g(f(y)) ==> f(x) = f(y) while g is onto. ==> x = y in A. i.e. whenever, (gof) (x) = (gof)(y) ==> x = y. thus, gof is a one to one function.

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