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Re: For all positive integers x, f(x)=f(x+1). If f(3)=15, then what is f(7 [#permalink]

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29 Jan 2015, 12:44

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It is given that: f(x) = f(x+1) implying, for any value of x, f(x) and f(x +1) has same value => this function is a constant value function. so for tis function, f(1) = f(2) = f(3) = .... = f(7) = ... f (n-1) = f(n) = 15. Hence, Ans is (C).

This problem really just comes down to understanding the function notation. If f(x)=f(x+1), that means that:

f(3)=f(3+1)=f(4) and that

f(4)=f(4+1)=f(5) and so on, meaning that really all functions equal the same thing as the next function up, so all functions are equal. That means that f(7) is the same thing as f(3), which we're told is 15. Therefore the answer is 15.
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