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Beginning Activity Beginning Activity 2: A Composition of Two Specific Functions
A4US

Let A={a,b,c,d} and let B={p,q,r,s}.

1.

Construct an example of a function f:A→B that is a bijection. Draw an arrow diagram for this function.

2.

On your arrow diagram, draw an arrow from each element of B back to its corresponding element in A. Explain why this defines a function from B to A.

3.

If the name of the function in Exercise 2 is g, so that g:B→A, what are g(p), g(q), g(r), and g(s)?

4.

Construct a table of values for each of the functions g∘f:A→A and f∘g:B→B. What do you observe about these tables of values?