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,(adsbygoogle = window.adsbygoogle || []).push({});

[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?

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

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