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Thread: Discrete Math PLEASE HELP!!

  1. #1
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    Discrete Math PLEASE HELP!!

    f(x) = (x+1)/(x+2)

    a) Determine if the function is injective

    b) Prove the answer to part a

    c) Determine if the function is surjective

    d) Prove the answer to part c
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  2. #2
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    Quote Originally Posted by jas05s View Post
    f(x) = (x+1)/(x+2)
    a) Determine if the function is injective
    $\displaystyle f(x_1) = f(x_2)\implies \frac{x_1+1}{x_1+2} = \frac{x_2+1}{x_2+2}$. Thus, $\displaystyle (x_1+1)(x_2+2) = (x_1 + 2)(x_2+1)$ this means $\displaystyle x_1x_2+x_2+2x_1+2 = x_1x_2+2x_2+x_1+2 \implies x_1 = x_2$.

    In general if $\displaystyle ab-cd\not = 0$ then $\displaystyle (ax+b)/(cx+d)$ is injective, try proving that.

    c) Determine if the function is surjective
    Yes. You need to show $\displaystyle \frac{x+1}{x+2} = y$ has a solution for any $\displaystyle y$, can you do that? And in general $\displaystyle (ax+b)/(cx+d)$ is surjective as well (try proving that too).
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