AnswersPBCSD_Grade_Forgiveness_1200710_Mathematics_for_College_Algebra_S1_2023Combinations and Separations of Functions

Composition of Functions Answers

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If p(x) = 2x2 – 4x and q(x) = x – 3, what is ?

Question illustration
A
2x2 – 4x + 12
B
2x2 – 16x + 18
C
2x2 – 16x + 30
D
2x2 – 16x + 15
2
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The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except –3. Which of the following describes the domain of ?

Question illustration
A
all real values except and the x for which
Option A
B
all real values except and the x for which
Option B
C
all real values except and the x for which
Option C
D
all real values except and the x for which
Option D
3

If and , what is the range of ?

Question illustration
A
mc021-4.jpg
Option A
B
mc021-5.jpg
Option B
C
mc021-6.jpg
Option C
D
mc021-7.jpg
Option D
4

Which description best explains the domain of ?

Question illustration
A
the elements in the domain of f(x) for which g(f(x)) is defined
B
the elements in the domain of f(x) for which g(f(x)) is not zero
C
the elements in the domain of g(x) for which g(f(x)) is defined
D
the elements in the domain of g(x) for which g(f(x)) is not zero
5

If and n(x) = x – 3, which function has the same domain as ?

Question illustration
A
mc019-3.jpg
Option A
B
mc019-4.jpg
Option B
C
mc019-5.jpg
Option C
D
mc019-6.jpg
Option D
6

If s(x) = x – 7 and t(x) = 4x2 – x + 3, which expression is equivalent to ?

Question illustration
A
4(x – 7)2 – x – 7 + 3
B
4(x – 7)2 – (x – 7) + 3
C
(4x2 – x + 3) – 7
D
(4x2 – x + 3)(x – 7)
7

For which pair of functions is ?

Question illustration
A
and
Option A
B
and
Option B
C
and
Option C
D
and
Option D
8

If h(x) = 5 + x and , which expression is equivalent to ?

Question illustration
A
mc003-3.jpg
Option A
B
mc003-4.jpg
Option B
C
mc003-5.jpg
Option C
D
5 + (5 + x)
9

If h(x) = x – 7 and g(x) = x2, which expression is equivalent to ?

Question illustration
A
(5 – 7)2
B
(5)2 – 7
C
(5)2(5 – 7)
D
(5 – 7)x2
10

If f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to ?

Question illustration
A
(3x + 2)(x 2 + 1)
B
3x 2 + 1 + 2
C
(3x + 2)2 + 1
D
3(x 2 + 1) + 2

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