3. consider the following statement.
"composition of functions is commutative."
is this statement always correct? if so, provide an example. if not, provide a
counterexample.

  rarely correct

  for f(x) = 6, g(x) = 2; f(g(x)) = 6, g(f(x)) = 2 ≠ f(g(x))

Step-by-step explanation:

The order in which functions operate on each other can rarely be reversed with the same result. If the functions are inverses of each other and both have the same domain as range, then their order can be reversed.

Not so, in most other cases. An example is shown above.

no not all of them.

step-by-step explanation:

some of them have a square base.

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.