Answer
$ An onto function is one whose range is the entire codomain. Thus we must determine whether we can write
every integer in the form given by the rule for f in each case.
a) Given any integer n, we have f(O, n) = n, so the function is onto.
b) Clearly the range contains no negative integers, so the function is not onto.
c) Given any integer m, we have f(m, 25) = m, so the function is onto. (We could have used any constant
in place of 25 in this argument.)
d) Clearly the range contains no negative integers, so the function is not onto.
e) Given any integer m, we have f(m, 0) = m, so the function is onto.
$ RESULT
a) Onto
b) Not onto
c) Onto
d) Not onto
e) Onto
Work Step by Step
$ An onto function is one whose range is the entire codomain. Thus we must determine whether we can write
every integer in the form given by the rule for f in each case.
a) Given any integer n, we have f(O, n) = n, so the function is onto.
b) Clearly the range contains no negative integers, so the function is not onto.
c) Given any integer m, we have f(m, 25) = m, so the function is onto. (We could have used any constant
in place of 25 in this argument.)
d) Clearly the range contains no negative integers, so the function is not onto.
e) Given any integer m, we have f(m, 0) = m, so the function is onto.
$
RESULT
a) Onto
b) Not onto
c) Onto
d) Not onto
e) Onto
