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

1. Sep 3, 2008

arroy_0205

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,
$$f(x)=x^{\frac{1}{3}}+\tanh^{-1}e^x+\sinh(\frac{1}{x})+x^x+x \log x$$
I think x appears explicitly.
$$x^y+y^x=1$$