2007-11-02

[離散][四版習題本] ch2 關係與函數 2-65 p123

題目如下
Use the fact every polynomial equation having real-number coefficients and
odd degree has a real root in order to show that the function f:R->R, defined by
f(x) = x^5 - 2x^2 + x, is an onto function. Is f one-to-one?

我的問題是題目給的odd degree 有何用意
麻煩各位幫我解答囉
謝謝~

2 則留言:

線代離散助教(wynne) 提到...

已知若一個實係數多項式具odd degree, 則它具有實根, 而在證明過程中, 因為g(x)符合上述條件 => g(x)具有實根, 之後再利用那個實根導出f:R->R為onto

Brian 提到...

ok ~
謝謝您喔~