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Grade: 12th pass
        
Let f: R -> R be a function that satisfies for all x,y € R
F(x+y)F(x-y) = [f(x) + f(y)]- 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
7 months ago

Answers : (1)

Aditya Gupta
1161 Points
							
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
7 months ago
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