Solution for Section 7.3 Question 1

1. In terms of an arrow diagram for a function:

• the function is one-to-one provided you do not have two arrows from different elements in the domain pointing to the same element in the co-domain;
• the function is onto provided that there is at least one arrow pointing to each element of the co-domain.

For the four functions given in the question:

• f is one-to-one and onto;
• g is neither;
• h is one-to-one but not onto;
• j is onto but not one-to-one.

Back to Section 7.3