Inverse of a function $f_k(x) := f (x ⊕ k) ⊕ k$ $f : \{0, 1\}^4 → \{0, 1\}^4$

Given a function $f_k(x) := f (x ⊕ k) ⊕ k$, what is the inverse function $f_k^{-1}$?

I could not figure out how this would be done. Thanks.
Assuming $f^{-1}$ exists (i.e., that $f$ is injective), then $$f_k^{-1}(y) = f^{-1}(y \oplus k) \oplus k.$$ To see why consider an $x \in \{0,1\}^4$ so that $f_k(x) = y$. Then you have that $$y \oplus k = f (x \oplus k).$$ Now by applying $f^{-1}$ on both sides of that equation you have $$f^{-1}(y \oplus k) = x \oplus k.$$ And finally by XOR'ing $k$ on both sides you get the above result.