come inlet F(x)=y
then x^3+x-y=0
这是一个比较简单（没有2次项）的三次方程
利用卡尔达洛公式（详情见
http://v15.huasing.org/bbs.php?A=03OikzM4cTOwATMioDO6M3OiQWafR3cvBnI6cjOztjI2ETMiozM6M3OiQWafRmch9mYioDO6M3Oic1TIN1XO9USUNUQioTMxozc7IibvlGdjFmI6YjOztjIUN1TQ9VRHFEUioTO6M3OiU2ZhBnI6QjOztnO0oTY
---posted by 逃课专家）
可以求出x
然后交换x,y即为原函数的反函数。。。
不过我还有一点不明白，是不是当三次方程没有2次项的时候，方程就只有一个实数解？？为什么？？高人指点。。。
try your question
firstly, if the cubic function is bijective, then of course it has an inverse. However, there is no direct relationship with the square term. Alternatively, you may check, if the original function is an increasing function, then definitely it has an inverse. You may use first derivative test to check it out. For example, X^3+x^2+4x+1=0, its first derivative is 3x^2+2x+4, and it's always positive, so, this function has an inverse although it has a square term.
Sorry, may have a lot of fallacies, pls enlighten me.:D
Sorry, may have a lot of fallacies, pls enlighten me.:D
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