Will this function be odd?

Question

Question: If $f:R\to R$ is an invertible function such that $f(x)$ and $f^{-1}(x)$ are symmetric about the line $y = -x$, then:

A) $f(x)$ is odd

B) $f(x)$ and $f^{-1}(x)$ may not be symmetric about $y = x$

C) $f(x)$ may not be odd

D) None of these

Purely by intuition, I'd say that $f(x)$ will be an odd function. Is this right? If it is, how can I prove this?