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

They are commutative, because f(x) and g(x) are constant functions.
They are commutative, because f(g(x)) and g(f(x) are constant functions.
They are not commutative, because f(x) and g(x) are not equal.
They are not commutative, because flg(x)) and g(f(x) are not equal.

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sqdancefan

Answer:

  They are not commutative, because f(g(x)) and g(f(x) are not equal.

Step-by-step explanation:

In order for the composition of the functions to be commutative, we must have ...

  f(g(x)) ≡ g(f(x))

for all values of x.

Here, we have f(g(x)) = 1 and g(f(x)) = 2. f(g(x)) and g(f(x)) are not equal, so the composition of the functions is not commutative.

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