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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?

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Want a 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.

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