On the premise that the definition domain is symmetrical about the origin,

F(-x)=f(x), and the function is even.

F(-x)=-f(x), and the function is odd function.

As long as the condition 1 is satisfied and the domain is symmetric about the origin; 2.f(-x)=f(x), and the function is even.

As long as the condition 1 is satisfied and the domain is symmetric about the origin; 2, f(-x)=-f(x), and the function is odd function.

Odd function is just an example of origin:

F(x)= 1/x, and the domain is (-∞, 0)U(0,+∞), which is symmetrical about the origin.

f(-x)= 1/(-x)=- 1/x =-f(x)

The function is odd function, but it is not the origin.

Example of even function but origin:

f(x)= 1/x？ , the domain is (-∞, 0)U(0,+∞), which is symmetrical about the origin.

f(-x)= 1/(-x)？ = 1/x？ =f(x)

Function is an even function, but it is not the origin.