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Math Help - Function problem.

  1. #1
    Senior Member Sambit's Avatar
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    Question Function 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?
    Last edited by mr fantastic; October 18th 2010 at 05:11 PM.
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  2. #2
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    I read the Wikipedia article on identity functions (assuming identity map and identity function are synonymous) and believe I can help.

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

    f(f(s)) = af(s) + b = a(as + b) + b = a^2s + ab + b<br />

    Solve the equation a^2s + ab + b = as + b for a and b.
    Last edited by mr fantastic; October 18th 2010 at 05:15 PM.
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