SAT I 一日一问：2014年6月19日

The correct answer is B

Explanation

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

However, if function f of n = n, then function f of (2 n) = 2 n = 2 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.

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