Composition of Functions Answers

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4

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
5

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
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)
8

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
9

If and h(x) = 4 – x, what is the value of ?

Question illustration
A
mc025-3.jpg
Option A
B
mc025-4.jpg
Option B
C
mc025-5.jpg
Option C
D
mc025-6.jpg
Option D
10

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

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