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Thread: Reading a function

  1. #1
    Aug 2007

    Reading a function

    okay, so i need to determine whether or not f is one-to-one and onto. if so, find f^-1.

    im pretty sure i can do it, i just dont know how to read the thing.

    A=R \ {0} and B=R \ {2} and f: A->B

    f(x)= 1/x + 2

    where R is the reals. can anyone please explain to me how to read that?
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  2. #2
    MHF Contributor red_dog's Avatar
    Jun 2007
    Medgidia, Romania
    $\displaystyle f:A\to B$ is bijective if and only if $\displaystyle \forall y\in B$, the equation $\displaystyle f(x)=y$ has an unique solution $\displaystyle x\in A$

    Now, let $\displaystyle y\in\mathbf{R}-\{2\}$

    $\displaystyle \displaystyle f(x)=y\Leftrightarrow \frac{1}{x}+2=y\Leftrightarrow \frac{1}{x}=y-2\Leftrightarrow x=\frac{1}{y-2}\in\mathbf{R}-\{0\}$
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