222 Mappings, Relations, and Functions
z (that is, we divide 1 by z). If z= 0, we say that q is not defined. If we let z be the
independent variable and q be the dependent variable, is this relation injective? Is it
surjective? Is it bijective?- Again, consider a relation between the set Z of integers and the set Q of rationals.
Imagine that this relation works in the same way as the relation in Prob. 7, but with one
exception. If z= 0, we say that q= 0 by default. If we let z be the independent variable
andq be the dependent variable, is this relation injective? Surjective? Bijective? - Consider the relation y=x^4 , where the domain is the entire set of reals and the range
is the set of nonnegative reals. Is this relation a function? If so, why? If not, why not?
Is the relation injective? Is it surjective? Is it bijective? - Imagine that the values of the independent and dependent variables in Prob. 9 are
transposed while leaving their names the same. Also suppose that the domain of the
new relation is the set of nonnegative reals, and the range of the new relation is the
entire set of reals. Is this inverse relation a function? If so, why? If not, why not? Is the
relation injective? Is it surjective? Is it bijective?