Show that $F$ in $F(\mathbf{x},y)=G(y,H_{1}(\mathbf{x}),H_{2}(y,\mathbf{x}))$ is recursive by giving a description of $F$, where $G,H_{1},H_{2}$ are recursive.
I have to find a description of $F$ to show $F$ is recursive. I was thinking that $H_{1}$ is using redundant variables, where $H_{1}'(\mathbf{x}, y) = H_{1}(\mathbf{x})$, which is primitive recursive, and $H_{2}$ is using permutation of variables, where $H'_{2}(\mathbf{x},y)=H_{2}(y,\mathbf{x})$, which is also primitive recursive. But this is as far as I can go. How do I describe $F$?