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

2. Originally Posted by jas05s
f(m,n)= m^2 - n^2

a) Determine if the function is injective

b) Prove the answer to part a
you must show whether or not $f(m_1,n_1) = f(m_2,n_2) \implies m_1 = m_2 \mbox{ and } n_1 = n_2$. if yes, it is injective.

c) Determine if the function is surjective

d) Prove the answer to part c
you must show whether or not for any $a \in f[ \mbox{dom}f]$ there are $m,n$ such that $f(m,n) = a$. (are m and n real numbers here?)