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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)]² - 4x²f(y)
 
Then 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
4 months ago

Answers : (1)

Arun
20299 Points
							
Dear student
 
put x = 0 = y
f(0)^2= 4 f(0)^2
 
hence f (0) = 0
 
now put y = x
 
0 = 4 f(x)^2 – 4 x^2 f(x)
 
f(x) = x^2
 
hence option 3 and 4 are incorrect
4 months ago
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