Show that the mapping f: R^{2}->R^{2}given by f(x,y)=(x+y,x-y) is linear.For each subspace X of R^{2 }describe f^{-->}(X) and f^{<--}(X).

My question is whetherfmeans that the image of the x-axis is the line y=x and the image of the y-axis is the line y=-x, so how am I describe^{-->}(X)f?^{<--}(X)

Thanks in advance.