+0  
 
0
94
2
avatar+75 

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
avatar+3628 
+2

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

.
 Oct 17, 2018
 #2
avatar+75 
+2

thank you

 Oct 17, 2018

27 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.