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@Apu
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.Draw a rough graph to get some intuition.
After this,
1. Consider the function g(x)=f(x+1/2)-f(x).
2. Since f(x) is continous the above function is also continous.
3. Plug in x=1/2 and x=0
4. g(1/2)=-g(0).
+solved @SirLancelotDuLac
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