find the value of 2 if f (x)=x2 in the interval [0, 2π]

V.Harikrishna naik
2022-06-07

find the value of 2 if f (x)=x2 in the interval [0, 2π]

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Suppose $f:{\mathbb{P}}^{2}\to {\mathbb{P}}^{2}$ is rational such that $f\circ f=\mathbb{I}\mathbb{d}$. Then is it true that $f$ must be linear?

It feels true due to the degree which increases, but some things might cancel out.

Suppose we have a smooth curve $C$ of genus $g\ge 1$ with a rational function $g:C\to C$ with the same property. Does it always rise to an $f$ on ${\mathbb{P}}^{2}$ whose restriction is $g$? Does it imply that $g$ has to be linear too? This on the other side seems wrong to me.

It feels true due to the degree which increases, but some things might cancel out.

Suppose we have a smooth curve $C$ of genus $g\ge 1$ with a rational function $g:C\to C$ with the same property. Does it always rise to an $f$ on ${\mathbb{P}}^{2}$ whose restriction is $g$? Does it imply that $g$ has to be linear too? This on the other side seems wrong to me.