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📅 April 30, 2026 👤 scraface

Apr 30, 2026

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Since \( f(x) \) is a rational function of degree \( \max(\deg ext{nu...
But since \( f(f(x)) \) is odd (as composition of odd functions), and...
Moreover, we know \( x = 0 \) is a solution.
Because \( f \) is odd and smooth, and \( f(f(x)) - x \) is odd, all s...
Letâs check degree: the leading term of \( f(x) \) is \( x \), so \(...
In fact, it is known in functional iterations that such rational funct...
But due to odd symmetry, solutions are symmetric about origin, so if \...
Now, \( f(f(0)) = f(0) = 0 \), so 0 is a solution.
Try numerical: \( f(1) = (1 - 3)/(1 + 1) = -2/2 = -1 \), \( f(-1) = ((...
Similarly, \( f(-1) = 1 \), so \( f(f(-1)) = f(1) = -1 = x \), so \( x...

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