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What is meant by implicit/explicit occurrence of a variable?

  1. Sep 3, 2008 #1
    I have not understood what precisely is meant when someone says for example, x occurs implicitly or explicitly in a given function. My vague idea is that if f(x) can be expressed solely as a function of x alone then x is said to be explicitly appearing. Is that correct? For exaple in,
    [tex]
    f(x)=x^{\frac{1}{3}}+\tanh^{-1}e^x+\sinh(\frac{1}{x})+x^x+x \log x
    [/tex]
    I think x appears explicitly.
    What about
    [tex]
    x^y+y^x=1
    [/tex]
    I think in this case it is incorrect to say that here x has explicit dependence in y(x). Can anybody make these precise or correct me if I am wrong?
     
  2. jcsd
  3. Sep 3, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    We should be able to write any function (of x) in the form y= f(x). In order to determine whether the y in xy+ yx= 1, you have to try to "solve for y". Whether you can or not, y is NOT and "explicit" function of x.
     
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