If R→R is is an invertible function such that f(x) and f-1x are symmetric about the line y=-x, then

Since f(x)  and  f-1x are symmetric about the line y = x. If  α,β lies on y=fx, then -α,-β lies on y=f-1x. Therefore, -α,-β lies on  y=fx.Hence, y=fx is  odd.