f(m,n)= m^2 - n^2
a) Determine if the function is injective
b) Prove the answer to part a
c) Determine if the function is surjective
d) Prove the answer to part c
you must show whether or not $\displaystyle f(m_1,n_1) = f(m_2,n_2) \implies m_1 = m_2 \mbox{ and } n_1 = n_2$. if yes, it is injective.
you must show whether or not for any $\displaystyle a \in f[ \mbox{dom}f]$ there are $\displaystyle m,n$ such that $\displaystyle f(m,n) = a$. (are m and n real numbers here?)c) Determine if the function is surjective
d) Prove the answer to part c