This is a question from functions. Please can anybody help. It's answer is 8, but how?
Devashish , 5 Years ago
Grade 12th pass
Algebra> This is a question from functions. Please...
1 Answers
Aditya Gupta
Last Activity: 5 Years ago
f(x)+f(x+4)= f(x+2)+f(x+6) holds for all real x. so replace x by x+2.
f(x+2)+f(x+2+4)= f(x+2+2)+f(x+2+6)
or f(x+2)+f(x+6)= f(x+4)+f(x+8)
now add the first equation and this eqn
f(x)+f(x+4)+ f(x+2)+f(x+6)= f(x+2)+f(x+6)+f(x+4)+f(x+8)
so that f(x)= f(x+8)
so period is 8. kindly approve :)
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