SAT I 一日一问：2013年5月20日

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)  

答案见下一页>>>

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.