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

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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(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

Arun · Answer

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

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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(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

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

1 Answers

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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(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

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)=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(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