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Image of a function

  1. Mar 29, 2012 #1
    1. The problem statement, all variables and given/known data
    find the image of the function
    h: (0,1)→ ℝ defined by h(x) = 1/(x2+8x) for 0<x<1


    2. Relevant equations



    3. The attempt at a solution
    I have tried a number of things, I can see the answer intuitively but I am having trouble with the proof. I set the function up as 1/(x2+8x)=b, and I have been trying to manipulate this in order to get what I need. the first thing i did was calculate b at x=0 (undefined) and x=1 (1/9) and from there I got 3 different intervals for b, the last one (1/9, ∞) i know is correct. I just am not sure how to show this is correct.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 30, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Here is one basic fact you need here- the fraction f(x)/g(x) is equal to 0 if and only if the numerator, f(x), is 0.
     
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