Problem Statement

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

Determine the domain of the function.

 
Step 1

Question Sequence

Question 1

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

where b = .

2
Incorrect
Correct

 
Step 2

We can write g(y) as a composition as

g(y) = (f º u)(y) = f(u(y))=

Question Sequence

Question 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 of u such that u(x) lies in the of f.

2
Incorrect
Correct

 
Step 3

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

Question Sequence

Question 3

is a(n) 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 4

The function is defined for y ≥ .

Correct.
Incorrect.

Question 5

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

Correct.
Incorrect.

Question 6

Therefore is defined when both and are defined. The domain of is

A.
B.
C.
D.
E.
Correct.
Incorrect.

 
Step 4

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

Question 7

Find the domain of . is a(n) function that is defined for all values of u.

Correct.
Incorrect.

Therefore, as long as is defined,

will be defined.

Question 8

So the domain of

is the same as the domain of :

A.
B.
C.
D.
E.
Correct.
Incorrect.