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Beginning Activity Beginning Activity 1: Functions and Sets
A4US

Let S={a,b,c,d} and T={s,t,u}. Define f:S→T by

f(a)=sf(b)=tf(c)=tf(d)=s.

1.

Let A={a,c} and B={a,d}. Notice that A and B are subsets of S. Use the roster method to specify the elements of the following two subsets of T:

(a)

{f(x)∣x∈A}

(b)

{f(x)∣x∈B}

2.

Let C={s,t} and D={s,u}. Notice that C and D are subsets of T. Use the roster method to specify the elements of the following two subsets of S:

(a)

{x∈S∣f(x)∈C}

(b)

{x∈S∣f(x)∈D}

Now let g:R→R be defined by g(x)=x2, for each x∈R.

3.

Let A={1,2,3,−1}. Use the roster method to specify the elements of the set {g(x)∣x∈A}.

4.

Use the roster method to specify the elements of each of the following sets:

(a)

{x∈R∣g(x)=1}

(b)

{x∈R∣g(x)=9}

(c)

{x∈R∣g(x)=15}

(d)

{x∈R∣g(x)=−1}

5.

Let B={1,9,15,−1}. Use the roster method to specify the elements of the set {x∈R∣g(x)∈B}.