Chapter 1.

1.1 Problem Statement

{3,5,7,9}
{1,2,4}

Determine the domain of the function.

1.2 Step 1

Question Sequence

Question 1.1

Recognize that g(y) is a FCdlRdNYB2S7WknmXfefRrJultvL5lMutmahGP0XQZsDFzxMXWmqaMVJndMnSJb0 of the functions and

where b = iSba6t70dtA=.

2
Incorrect
Correct

1.3 Step 2

We can write g(y) as a composition as

g(y) = (f º u)(y) = f(u(y))=

Question Sequence

Question 1.2

Recall how to find the domain of a composition function (f º u)(x) = f(u(x)).

The domain of (f º u) is the set of values of x in the 7qSkmY1eVWXSxa8Dy2/N38Gq1Rw= of u such that u(x) lies in the 7qSkmY1eVWXSxa8Dy2/N38Gq1Rw= of f.

2
Incorrect
Correct

1.4 Step 3

Find the values of y that are in the domain of .

Question Sequence

Question 1.3

The function is a(n) yT8b6AGIZM8Xq6I+3rIMpf8ZiVSiQojW2i3bJdvyICJGuPXUX3A6azujumEslbYbW/EIZQ== function, so a value of y belongs to the domain of u(y) if u is defined for that y-value.

2
Correct.
Incorrect.

Question 1.4

The function is defined for y ≥ iSba6t70dtA=.

Correct.
Incorrect.

Question 1.5

The function is defined for all values of y except y = 1Wh3cvJ2xF4=.

Correct.
Incorrect.

Question 1.6

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
Correct.
Incorrect.

1.5 Step 4

Find the values of y in the domain of u such that u(y) is in the domain of

Question 1.7

Find the domain of . The function is a(n) WLUzp4xCiPh5d+pw5TbLGXpwCSN3Cqy3DpUpYsDr78Hfn4Q4tf9NBiKRTu20Bo7DsowmpA== function that is defined for all values of u.

Correct.
Incorrect.

Therefore, as long as is defined,

will be defined.

Question 1.8

So the domain of

fAFoQOdtpI85HAmxul7oU9uR9FIp7lzRI7/0J6zyrfG7GC1XgXkMqZ7HwoV9uzz89i0D2BmUczDwRBapPEU437Tiuyom+4P9MZyN6fdzf3DejkPTkqTqc/yNGxZLVbTMZQuGpGXB9U7gnijpUFEW60XOYAuJ3OGObhLQk9bie2Pb7+xZDXRuYGljW/ddMVXtX5EWZvmnYdp1BthVEfCzfpukRqwfiWYHRhiJibfou3hncmCe3C7CQ3o6gYv74c0cCF0FFTwpN5Qekbj7XMe20M2hXVSkoRttL7XNK1+7gjtDJybcH4Hr47sj0Y0d08uA015tge7afYrAbauocmiEtUhf2ZQObREzZkV+6MJq0b0f8tVpQnNNjBfwYy1UNq5brwRfy54lLgZQqKV8TdyxeRyEeUg7eO+oEOyQ9vUMXSK9TuBBfZuKLlyzOXk=
Correct.
Incorrect.