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Thread: Injective Function

  1. #1
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    Injective Function

    Let f: R-{-2} -> R defined by f(x)=(2x-1)/(x+2)

    Prove that f is injective. Thank you.
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  2. #2
    Senior Member vincisonfire's Avatar
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    In this kind of question you first set $\displaystyle f(a) = f(b) $
    Here it gives $\displaystyle \frac{2a-1}{a+2} =\frac{2b-1}{b+2}$.
    And you juggle with a and b to show that $\displaystyle f(a) = f(b) $ implies a=b.

    $\displaystyle (2a-1)(b+2) =(2b-1)(a+2)$

    $\displaystyle 2ab+4a-b-2 =2ab+4b-a-2$

    $\displaystyle 4a-b=4b-a$

    $\displaystyle 5a=5b$

    $\displaystyle a=b$
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