Let f : N `to N : f(x) =2 x` for all `x in N` Show that f is one -one – InterviewSolution

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1.	Let f : N `to N : f(x) =2 x` for all `x in N` Show that f is one -one and into.
Answer» We have `f(x_(1)) = f(x_(2)) rArr 2x_(1) =2 x_(2) rArr x_(1) = x_(2)`. `:. ` f is one - one Let y =2x . Then `x=(y)/(2).` If we put y=3 then `x=(3)/(2) in N` Thus `3 in N` has no pre-image in N `:.` f is into Hence f is one-one and into .

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