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Determine the function satisfying f^2(x+...

Determine the function satisfying `f^2(x+y)=f^2(x)+f^2(y)AAx ,y in Rdot`

Text Solution

Verified by Experts

The correct Answer is:
`f(x)=0`
Given `f^(2)(x+y)=f^(2)(x)+f^(2)(x)+f^(2)(y).`
Put `x=y=0.` Therefore,
`f^(2)(0)=f^(2)(0)+f^(2)(0)`
` :. f(0)=0`
Now, replace y by -x. Therefore,
`f^(2)(0)=f^(2)(x)+f^(2)(-x)`
or `f^(2)(x)+f^(2)(-x)=0`
` :. f(x)=0`
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