The inverse scale function has three axes of symmetry

The inverse scale function has three axes of symmetry

The inverse scale function y = 1 / X is only symmetric about the origin, not about the coordinate axis
But it is symmetric with respect to the lines y = x and y = - X

High school mathematics, both odd and even functions
Is there only one case where f (x) = 0 for odd and even functions? If there are others, please give a counter example

F (x) = - f (- x) f (x) = f (- x) f (x) = - f (x) 2F (x) = 0f (x) = 0, three elements of function, corresponding rule, domain, range corresponding rule is the only case, the range is {0}, but the domain only needs to be symmetrical about the origin. There are countless cases of domain, so there are countless functions. For example, f (x) = 0, X: [- 2,2

A mathematics problem in Senior One: even function defined on R is known
Given that f (x) is an odd function defined on R, G (x) is an even function defined on R, and f (x) - G (x) = 1-x ^ 2-x ^ 3, then G (x) =?

[answer] f (x) = - X & sup3;, G (x) = x & sup2; - 1
[analysis]
f(x)-g(x)=1-x²-x³－－－(1)
f(-x)-g(-x)=1-(-x)²-(-x)³=1-x²+x³
Since f (x) is an odd function, f (- x) = - f (x)
Since g (x) is an even function, G (- x) = g (x)
-f(x)-g(x)=1-x²+x³－－－(2)
(1) + (2) get
-2g(x)=2-2x²
g(x)=x²-1
So f (x) = g (x) + (1-x & sup2; - X & sup3;) = - X & sup3;