A) \( F(x)=\operatorname{cog}_{3}(x+3)+3 \)

It seems like you're referring to a function \( F(x) \) that involves the "cog" function, which is not a standard mathematical term. However, if we interpret "cog" as the ceiling function (often denoted as \( \lceil x \rceil \)), we can proceed with that assumption. Assuming \( \operatorname{cog}_{3}(x) \) refers to the ceiling function with a base of 3, we can express it as: \[ \operatorname{cog}_{3}(x) = \lceil x \rceil \] Thus, the function \( F(x) \) can be rewritten as: \[ F(x) = \lceil x + 3 \rceil + 3 \] This function takes an input \( x \), adds 3 to it, applies the ceiling function, and then adds another 3. If you have a specific question or need further clarification about this function, please let me know!