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    Functions: Mapping

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    For the functions f defined below, determine which are 1:1, onto or both.

    1) f: R onto R, f(x) = |x|

    2) f: R onto R, f(x) = x^2 + 3

    3) f: R onto R, f(x) = x^3 + 3

    4) f: R onto R, f(x) = x(x^2-4)

    5) f: R onto R, f(x) = |x| + x

    6) f: N onto N, f(x) = x + 1

    7) f: N onto NxN, f(x) = (x,x)

    8) f: NxN onto N, f(x,y) = 2x + y

    9) f: R^2 onto R^2, f(x,y) = (x+y , x-y)

    10) f: R^2 onto R^2, f(x,y) = (x+y , x^2-y^2)

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    https://brainmass.com/math/graphs-and-functions/functions-mapping-11368

    Solution Preview

    1) f: R onto R, f(x) = |x|
    No. because f(-x) = f(x)

    2) f: R onto R, f(x) = x^2 + 3
    No. because f(-x) = f(x)

    3) f: R onto R, f(x) = x^3 + 3
    Yes, we can never find f(a)=f(b) if a isn't equal b

    4) f: R onto R, ...

    Solution Summary

    The mapping of functions is investigated.

    $2.49

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