If the real normalized functions f(x) and g(x) are not orthogonal, show that their sum f(x) +g(x) and their difference f(x)−g(x) are orthogonal.
If two functions are orthogonal, then their scalar product is equal to zero. Let's check:
As far as f(x) and g(x) are normalized,
Thus, obtain:
Hence, functions f(x) +g(x) and f(x)−g(x) are orthogonal.
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