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Does f(x)^g(x) have a name?

  1. May 17, 2012 #1
    I was trying to explain to someone how to find limit of function in form of [tex]f(x)^{g(x)}[/tex] and was asked what kind of function it is. I don't know if this function has a name. Does "power-exponential" sound right?

    Thanks!
     
  2. jcsd
  3. May 17, 2012 #2
    Depending on the range of ##g##, this expression may or may not make sense if ##f## is ever negative. So without knowing much about ##g## we need to say that ##f## is always strictly positive.

    Then ##f(x)^{g(x)}=e^{\log f(x)^{g(x)}}=e^{g(x)\log f(x)}## is really built from elementary functions. I am not aware of this brand of function being given a special name. I suppose you can name it whatever you want.

    As long as we're building interesting functions and naming them, what name would you give to ##\log_{f(x)}g(x)##?
     
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