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# What is the value of f(n/2)?

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Let f(x) be a function such that, for every real number x,f(x)+2f(-x) = sin x. What is the value of f(n/2)?

Oct 17, 2018

#1
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$$f(x)+2f(-x)=\sin(x)\\ f(-x)+2f(x) = \sin(-x) = -\sin(x) \\ \text{add these two equations} \\ 3(f(x)+f(-x)) = 0\\ f(-x)=-f(x)\\ f(x) -2f(x) = \sin(x) \\ -f(x) = \sin(x)\\ f(x) = -\sin(x) \\ f\left(\dfrac n 2\right) = -\sin\left(\dfrac n 2\right)$$

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Oct 17, 2018
#2
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thank you

Oct 17, 2018