Accuplacer Composition of Functions — practice questions

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_

1. A composition works from the inside out, so evaluate g first. 2. Substituting 2 into g gives 2 squared plus 2. 3. That is 4 plus 2, which is 6. 4. Now feed 6 into f as its input. 5. Substituting 6 into f gives 3 times 6 minus 1. 6. That is 18 minus 1, which is 17. 7. The answer 27 evaluates g(f(2)) instead, reversing the order of the two rules. 8. The answer 25 squares the result of f rather than composing in the stated order. 9. The answer 11 stops at f(2) and never uses g at all. _Source: OpenStax College Algebra (CC BY 4.0), section 3.4 Composition of Functions_