Question

Determine whether function f : Z × Z → Z is onto if (i) f(m,n)=2m−n

(ii) f(m,n)=m+n+1

Answer 1

onto function is a function f that maps an element x to every element y

i)

the function $f(m,n)=2m−n$ is onto

we can express every element y (every integer) by this function:

$f(0,n)=-n$, where n is integer

ii)

the function $f(m,n)=m+n+1$ is onto

we can express every element y (every integer) by this function:

$f(-1,n)=n$, where n is integer