show that inverses $\pi_{1},\pi_{2}$ are recursive?

Question

show that one can define inverses $\pi_{1},\pi_{2}$ for $ \langle.,.\rangle$ with$\pi_{1}(\langle m,n \rangle)=m,\pi_{2}(\langle m,n \rangle)=n\ \ \forall n,m$ wich are also recursive?

Answer 1

(Assuming that $\langle\cdot,\cdot\rangle$ means the Cantor pairing function.)

HINT: If $\langle m,n\rangle=k$ then $m,n\leq k$.