Question

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.

Answer 1

Sometimes correct

Explanation:

Answer 2

rarely correct

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

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.