Question of the Day

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6/1

Nov
20
2012
215,850 responses
Question of the Day Statistics
Number Answered
Correct 100,151
Incorrect 115,699
46% correct

Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

  • function f of (2 times n) = 2 times function f of n for all integers n
  • function f of 4 = 4

If function f is a function defined for all positive integers n, and function f satisfies the two conditions above, which of the following could be the definition of function f?

Answer Choices

Hint

It is easy to check whether function f of 4 = 4 for the functions given. First, eliminate those functions for which function f of 4 is not equal to 4. Then evaluate the functions for some values, such as n = 1 or n = 2, to see whether function f of (2 times n) = 2 times function f of n for those values.

Question of the Day

Can you answer today's question?

Register Next Tests:
6/1

Nov
20
2012
215,850 responses
Question of the Day Statistics
Number Answered
Correct 100,151
Incorrect 115,699
46% correct

Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

  • function f of (2 times n) = 2 times function f of n for all integers n
  • function f of 4 = 4

If function f is a function defined for all positive integers n, and function f satisfies the two conditions above, which of the following could be the definition of function f?

Answer Choices

Answer

If function f of n = n minus 2, then function f of 4 = 4 minus 2 = 2 does not equal 4, so the second condition fails. If function f of n = 2 times n, then function f of 4 = 8 not equal to 4, so the second condition fails for this function also. The other three options satisfy function f of 4 = 4, so it remains to check whether they satisfy the first condition.

If n = 1, and function f of n = 4, then function f of (2 times n) = function f of 2 = 4 and 2 times function f of 1 = 2 times 4 = 8, so it is not true that function f of (2 times n) = 2 times function f of n for all integers n. This means that the function function f of n = 4 does not satisfy the first condition. If n = 1, and function f of n = (2 times n) minus 4, then function f of (2 times n) = function f of 2 = (2 times 2) minus 4 = 0 and 2 times function f of n = 2 times function f of 1 = 2 times negative 2 = negative 4, so it is not true that function f of (2 times n) = 2 times function f of n for all integers n. This means that the function function f of n = (2 times n) minus 4 does not satisfy the first condition.

However, if function f of n = n, then function f of (2 times n) = 2 times n = 2 times function f of n, for all integers n. Also, function f of 4 = 4. Therefore, the function function f of n = n is the only option that satisfies both conditions.