A question asked today made me think of this case :
$f(x^{-1})$ = $\left(f(x)\right)^{-1}$.
Apparently the function ($x^2$) , for example, satisfies this condition. So does the absolute value function. Maybe I should ask whether there is some function that does not have this property.
Is this property of any interest and has it received a name?
The formula reminds me of the definition of " isomorphism" ( " the image of the product is the product of the images"). Is this purly accidental?
Here the " operation" would be unary and would be " inversion".