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 - 4x 2 f(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

Question

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 - 4x 2 f(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

Aditya Gupta · Answer

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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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 - 4x 2 f(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

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

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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 - 4x 2 f(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

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

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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