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Homework Help: Solve the equation

  1. Sep 18, 2010 #1
    1. The problem statement, all variables and given/known data
    Hello, I'm having some trouble with the following problem:

    Solve y = x+[tex]\frac{1}{x}[/tex] for 0 < x [tex]\leq[/tex] 1

    2. Relevant equations

    y = x+[tex]\frac{1}{x}[/tex] for 0 < x [tex]\leq[/tex] 1

    3. The attempt at a solution

    I am not sure on how to start. I've spent a lot of time thinking about how to this problem, but have had no luck. The only thing comes to mind is that y = [tex]\frac{x}{x}[/tex] + [tex]\frac{1}{x}[/tex] = 1. This solution seems to trivial; I would greatly appreciate any help.

    Thank you.
  2. jcsd
  3. Sep 19, 2010 #2


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    Homework Helper

    I'll assume the question instead means find the range of the function for the domain 0<x<1.

    Are you allowed to use calculus?

    I would start by finding the limit of y as x approaches 0+ and find y when x=1. If you can't use calculus then it will probably suffice to just explain that as x increases in that interval, y is always decreasing. This is enough information to give the range.
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