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Why is the composition f(g(x)) different from the product f(x) times g(x)?
AOne reverses the order of terms
BOne adds the two outputs first
COne feeds an output into a rule
DOne divides the two rules
Answer & Solution
Correct answer: C. One feeds an output into a rule
1. A product multiplies the two outputs that f and g give for the same input.
2. A composition instead feeds the output of g in as the input of f.
3. Those are different operations and usually give different results.
4. The order matters too, so f(g(x)) and g(f(x)) are usually different as well.
_Source: OpenStax College Algebra (CC BY 4.0), section 3.4 Composition of Functions_
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