Is There a Function That Always Results in a Positive Sign?

[Jhenrique]

"Geometric absolute"

If exist a function called absolute that ensures that the result have always the posite sign, so, exist some function that ensures that the sign of the result is always ×?

$f(x) = x$
$f(\frac{1}{x}) = x$

 

[homeomorphic]

The question does not make sense as stated. x is not a sign.

The first equation defines a function f(x) = x, and the function that satisfies the 2nd equation is 1/x, but obviously, there is no function that satisfies both.