Let, f:Z-->Z be a function defined by:- f(s)= as + b , for certain integers a and b. Then, for what values of a and b, f○f will be anidentity map?

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- Oct 18th 2010, 07:47 AMSambitFunction problem.
Let, f:Z-->Z be a function defined by:- f(s)= as + b , for certain integers a and b. Then, for what values of a and b, f○f will be an

__identity map__? - Oct 18th 2010, 08:07 AMNOX Andrew
I read the Wikipedia article on identity functions (assuming identity map and identity function are synonymous) and believe I can help.

$\displaystyle f(x)$ is an identity function if $\displaystyle f(x) = x$. Therefore, $\displaystyle f(f(s))$ is an identity function if $\displaystyle f(f(s)) = f(s)$.

$\displaystyle f(f(s)) = af(s) + b = a(as + b) + b = a^2s + ab + b

$

Solve the equation $\displaystyle a^2s + ab + b = as + b$ for $\displaystyle a$ and $\displaystyle b$.