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Beginning Activity Beginning Activity 1: Constructing a New Function

Let A={a,b,c,d}, B={p,q,r}, and C={s,t,u,v}. The arrow diagram in Figure 6.23 shows two functions: f:AB and g:BC.

Notice that if xA, then f(x)B. Since f(x)B, we can apply the function g to f(x), and we obtain g(f(x)), which is an element of C.

Using this process, determine g(f(a)), g(f(b)), g(f(c)), and g(f(d)). Then explain how we can use this information to define a function from A to C.

Figure 6.23. Arrow Diagram Showing Two Functions