An algebra problem by Anandmay Patel

Algebra Level 3

Find all functions \(f: \mathbb{R} \rightarrow \mathbb{R}\) that satisfy: \[f(x+y)^2=f(x)^2+f(y)^2\] Then the function is a \(\text{ _________} \) function.

Bonus: Investigate some properties of the function

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