如何判断$\Bbb R$上的一个多项式$P(x)$是双射?

hbghlyj

How does one show that a given polynomial is bijective?
首先$n=\deg P$是奇数.
$P(x)=ax+b\;(a\ne0)$是双射.
$P(x)=ax^3 + bx^2 + cx + d\;(a\ne0,3ac\ge b^2)$是双射.
对于$n\ge5$情况呢?

hbghlyj

FunctionBijective 2020 年 (12.2)

1. FunctionBijective[x^3 + a x + b, x]

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输出
ConditionalExpression[True, (a | b) ∈ Reals && a > 0]
resources.wolframcloud.com/FunctionRepository … s/FunctionJectivity/