Final answer:
The correct statement about functions is Option B: If f and g are functions, then f(x) + g(x) = g(x) + f(x), which is true due to the commutative property of addition that applies to the addition of functions too.
Step-by-step explanation:
The question asks which of the given statements about functions is true. When assessing the options provided, we can utilize the commutative and associative properties of addition and multiplication, as well as the properties of function composition. Now, let's examine the correct statement.
Option B states that if f and g are functions, then f(x) + g(x) is equal to g(x) + f(x). This is true due to the commutative property of addition, which holds for addition of functions as it does for ordinary numbers, meaning that f(x) + g(x) is always equal to g(x) + f(x). The other options can be dismissed as follows:
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- Option A is generally false because function composition is not commutative; (f∘g)(x) is not necessarily equal to (g∘f)(x).
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- Option C is true because the multiplication of functions is commutative, similar to the multiplication of numbers, so f(x) ⋅ g(x) equals g(x) ⋅ f(x).
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- Option D is typically false since subtraction is not commutative in general, meaning f(x) - g(x) is not equal to g(x) - f(x) unless f and g are specifically such that their difference gives the same result regardless of order, which is not true in general.
Therefore, the correct answer is Option B: If f and g are functions, then f(x) + g(x) = g(x) + f(x).