$$f(x)=0$$ and $$g(y)=0$$

$$f(x)=g(y)=$$ constant

$$f(x)\ne$$ constant and $$g(y)\ne$$ constant

$$f(x)+g(y)=f(x)-g(y)$$

Operation 1 : A clockwise rotation by 90$$^\circ$$ about an axis perpendicular to the plane of the figure

Operation 2 : A reflection along a horizontal line

Operation 1 : A counter clockwise rotation by 90$$^\circ$$ about an axis perpendicular to the plane of the figure

Operation 2 : A reflection along a vertical line

Operation 1 : A clockwise rotation by 90$$^\circ$$ about an axis perpendicular to the plane of the figure

Operation 2 : A reflection along a vertical line

Operation 1 : A counter clockwise rotation by 180$$^\circ$$ about an axis perpendicular to the plane of the figure

Operation 2 : A reflection along a vertical line