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Is this undefined?

  1. Mar 8, 2010 #1

    Mentallic

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    If I'm asked to graph this function: [tex]y=\frac{1}{x^{-1}}[/tex]

    Is x=0 undefined? Obviously by the rule of powers, this equation is the same as y=x, but I'm unsure if the point (0,0) exists in this equation or not.
     
  2. jcsd
  3. Mar 8, 2010 #2
    That function is not defined at x=0. To simplify it to x, you rely on the fact that you can multiply by 1=x/x. But x/x isn't defined when x=0, so you can't use simplification to get around the undefinedness at 0.
     
  4. Mar 8, 2010 #3

    Mentallic

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    Yes, if I converted the power to a fraction as so: [tex]\frac{1}{\frac{1}{x}}[/tex] then I'd be relying on that rule, but what about if I used the rule of powers, i.e. [tex]\frac{1}{x^a}=x^{-a}[/tex] So simply, [tex]\frac{1}{x^{-1}}=x^{-(-1)}=x[/tex]

    It just seems to me that only sometimes this is undefined, depending on how you treat the problem.

    Sort of like [tex]\sqrt{x^2}=|x|[/tex] while [tex](\sqrt{x})^2=x[/tex] and defined for only [itex]x\geq 0[/itex]
     
  5. Mar 8, 2010 #4
    That rule explicitly requires [tex]x\ne0[/tex].
     
  6. Mar 8, 2010 #5

    Mentallic

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    Ahh yes, of course!

    Thanks tinyboss :smile:
     
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