Mathematics > Standard Multiple Choice
Read the following SAT test question and then click on a button to select your answer.
- for all integers
If is a function defined for all positive integers , and satisfies the two conditions above, which of the following could be the definition of ?
(A)
(B)
(C)
(D)
(E)
The Correct answer is B.
Explanation
If , then , so the second condition fails. If ,then , so the second condition fails for this function also. The other three options satisfy , so it remains to check whether they satisfy the first condition.
If , and , then and , so it is not true that for all integers . This means that the function does not satisfy the first condition. If , and , then and , so it is not true that for all integers . This means that the function does not satisfy the first condition.
However, if , then , for all integers . Also, .Therefore, the function is the only option that satisfies both conditions.