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Math Help - surjectivity

  1. #1
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    surjectivity

    given that the function f(x) = l log x l where the domain is (0, infinity) and the range is real numbers. may i know why is the function not surjective?

    thanks
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  2. #2
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    [quote=alexandrabel90;505619]given that the function f(x) = l log x l where the domain is (0, infinity) and the range is real numbers. may i know why is the function not surjective?

    if y has an inverse y^{-1} : R->(0 to infinity)
    y = |log (x)|
    e^{y} = e^{ log x}
      x = e^{y}
    surjective = the range is equal to the codomain
    simply because y can only take positive values, so there are some elements in range(R) which are not covered
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  3. #3
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    Quote Originally Posted by alexandrabel90 View Post
    given that the function f(x) = l log x l where the domain is (0, infinity) and the range is real numbers. may i know why is the function not surjective?

    thanks

    The range is (-\infty,\infty). Now what does f(x) = -10 map to in the domain?
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