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    Onto and one-to-one

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    Which functions are one-to-one? Which functions are onto? Describe the inverse function

    A)F:Z^2-N where f is f(x,y) x^2 +2y^2
    B)F:N->N where f is f(x) = x/2 (x even) x+1 (x odd)
    C)F:N->N where f is f(x) = x+1 (x even) x-1 (x odd)
    D)h:N^3 -> N where h(x,y,z) = x + y -z

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    Solution Preview

    <br>A) f is not one-to-one since f(-1,1)=f(1,1)=3. f is not onto since f(x,y)=x^2+2y^2=2 has no integer solutions. There is no inverse function.
    <br>B) f is onto since for each n in N, we have f(2n)=2n/2=n. f is not one-to-one since f(4)=4/2=2 and ...

    Solution Summary

    This shows how to identify inverse, one-to-one, and onto functions.