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

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 . 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

Itk6c6KA79VXpQgLX4P6yHJ0yTRbZkmOnonZjv4o12yXHBSDxe3kvgITPSgLaUwbxrflZ8PdZTecHSube7K78IQJDpeZ/lnf4hYJQT4Kb4374hdaH0dr9my9mEfzhBa8JYwfTnqj4vQv8Zpvpk9hip14gE4j06hDRoXwnY6qA5Jm+fhevuhPx1Dq50AETOV+Odc7Enic8PH0wYG+mC+yIXzMEUCqX+PmPnUG3YquNrFPktFlF/AWKBGT0ibdtmphfDw+vOzYGJM4rORNfv5QgeTKRMxHbtvU4tm2Vpw1jVOGh26OPuStOnbMvxifXo6tCzYm9a2mcNESOsOz70f8Jt0BImNnG5/dIIvGLEOgBEwBlY6sprEEXA==
Correct.
Incorrect.