NandishSS wrote:If x is a positive integer, f(x) is defined as the number of positive integers which are less than x and do not have a common factor with x other than 1. If x is prime, then f(x)=?
A. x−2
B. x−1
C. (x+1)/2
D. (x−1)/2
E. 2
Let x = 2.
f(2) = the number of positive integers that are
less than 2 and that do not share a factor with 2 other than 1.
Only one positive integer satisfies the conditions in red: 1.
Thus:
f(2) =
1.
Now plug x=2 into the answers to see which yields the target value in blue.
Only
B works:
x-1 = 2-1 = 1.
The correct answer is
B.
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