Let $f$ be the function defined by $f(x)=\sin 3 x+\cos 6 x$ and let $g$ be the function defined by $g(u)=\sin 3 u+\cos 6 u$, for all real numbers $x$ and $u$.

Mark all true items with a check. There may be more than one correct answer.

A. $f$ and $g$ are exactly the same functions.

B. If $x$ and $u$ are different numbers, $f$ and $g$ are different functions.

C. Not enough information is given to determine if $f$ and $g$ are the same.

In the answer box below, explain your reasoning for each of the three choices you made above. Use complete sentences and correct grammar, spelling, and punctuation. Be specific and detailed. Write as if you were explaining the answer to someone else in class.