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Math Help - 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  f(a) = f(b)
    Here it gives  \frac{2a-1}{a+2} =\frac{2b-1}{b+2}.
    And you juggle with a and b to show that  f(a) = f(b) implies a=b.

     (2a-1)(b+2) =(2b-1)(a+2)

     2ab+4a-b-2 =2ab+4b-a-2

     4a-b=4b-a

     5a=5b

     a=b
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