5
QuizMultiple Choice

Composition of Functions and Modeling

Question 5 • GA-GSE Pre-Calculus

Are the compositions of f(x) = 1 and g(x) = 2 commutative? Why or why not?

Answer
A
They are commutative, because f(x) and g(x) are constant functions.
B
They are commutative, because f(g(x)) and g(f(x) are constant functions.
C
They are not commutative, because f(x) and g(x) are not equal.
D
They are not commutative, because f(g(x)) and g(f(x) are not equal.

Explanation

Since f(x) = 1 for every input, f(g(x)) = 1. Since g(x) = 2 for every input, g(f(x)) = 2. These compositions are not equal, so the compositions are not commutative; choice D states this reason.

AI-written and checked against the verified answer.

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