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question mark

Let f: R -> R be a function that satisfies for all x,y € R
F(x+y)F(x-y) = [f(x) + f(y)]2 - 4x2f(x)
Which of the following is not possible for f ?
A) f(0)=0
B) f(3)=9
C) f(5)=0
D) f(2)=2

Vaibhav Jain , 7 Years ago
Grade 12th pass
anser 1 Answers
Aditya Gupta
First of all put x=y= 0, and you will see that f(0)= 0. Now put y=0 and let x remain x. Then you will will get 4x^2f(x)=0 or f(x)=0
Hence, f is identically zero. Therefore option B and D are not possible
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