F(x) and g(x) images are symmetrical about the origin, which shows that:

For each point P(x, y) on the image of the function f(x),

There is a unique point P'(-x, -y) on the function g(x).

For example, the function f(x)=x+ 1, and the line symmetrical to the origin is:

-y=-x+ 1, that is g(x)=x- 1.

Verification: If point (0, 1) is selected on f(x), then (0,-1) must be on g(x)=x- 1, and the verification is consistent.