Let's combine composition with the properties you learned in algebra during the first week.Think about the property of commutativity.We know thatboth addition and multiplication are commutative operations because the order in which we multiply or add is unimportant, the answer will be the same.( 6 x 7 = 7 x 6;4 + 8 = 8 + 4).

Now, let's bring in composition.I claim that composition is not a commutative operation!Why?Well, let's think of a silly real-world example.

If f(x) = putting on your pants in the morning, and if g(x) = putting on your underwear, then(fg)(x) = f(g(x))= underwear first, then pants; AND ( gf)(x) = g(f(x)) = pants first, THEN underwear!This means you are wearing your underwear on top of your pants- VERY different than wearing your pants on top of your underwearThisshows us that(fg)(x) IS NOT EQUAL to (gf)(x), and therefore does not represent a commutative operation.

Your turn.Come up with an example to show that the property of composition is NOT a commutative operation.Be creative.You can either come up with real-world functions, or alternatively, you can use algebra as well, but let me know that you can prove that the property of composition does not represent a commutative operation.When you are finished with your example, comment on someone else's example.