Chapter 2: Q77E (page 155)
For each of these partial functions, determine its domain, codomain, domain of definition, and the set of values for which it is undefined. Also, determine whether it is a total function.
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Which function in exercise 12 is onto?
explain what it means for one set to be a subset of another set. How do you prove that one set is a subset of another set?
a) Define what it means for a function from the set of positive integers
to the set of positive integers to be one-to-one
b) Define what it means for a function from the set of positive integers to the set
of positive integers to be onto.
c) Give an example of a function from the set of positive integers to the set of
positive integers that is both one-to-one and onto.
d) Give an example of a function from the set of positive integers to the set of
positive integers that is one-to-one but not onto.
e) Give an example of a function from the set of positive integers to the set of
positive integers that is not one-to-one but is onto.
f) Give an example of a function from the set of positive integers to the set of
positive integers that is neither one-to-one nor onto.
Determine whether is onto if
Show that the function from the set of real numbers to the set of non-negative real numbers is not invertible, but if the domain is restricted to the set of non- negative real numbers, the resulting function is invertible.
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