Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

? asked in 科學數學 · 2 decades ago

有理函數( rational function )是什麼

請問有理函數 ( rational function )是什麼? 能舉些例子? 如果有平方根的還可以算是rational function嗎?

Update:

即將若x在√內就不算是rational function嗎..?

嗚...那麼我在考試答錯了..QQ

1 Answer

Rating
  • ?
    Lv 6
    2 decades ago
    Favorite Answer

    先提一下多項式:形如p(x) = anxn+an-1xn-1+…+a1x+a0(其中n是正整數或0;an,an-1,…,a1,a0都是實數),的式子稱為x的多項式。若n≠0,則稱p(x)為n次多項式。若n=0,a0≠0,則稱p(x)為零次多項式。若n=0,a0=0,則稱p(x)為零多項式。零次多項式與零多項式統稱為常數多項式。例:√2x3+1/ 2x2+ 2x - 2  為 3次多項式。(- 2即+(- 2))x - 1 為 1次多項式。5為 零次多項式。(5可以寫成5x0)多項式可以p(x)、f(x)、g(x)、h(x)等符號表示。再介紹有理函數:形如f(x) =g(x)/h(x) 的函數(其中g(x)、h(x)是多項式;h(x)≠0),稱為有理函數。當h(x) 為零次多項式時,f(x) 即為多項函數。當f(x) = c(c是實數),f(x) 稱為常數函數。常數函數是多項函數的一種,多項函數又是有理函數的一種。常數函數、多項函數、有理函數統稱為代數函數。例:以下皆是有理函數:f(x) = 0f(x) = √2f(x) = ex3+ln 2x2+sin60∘x+πf(x) = 2/(x+3)f(x) = (2x-1)/(x2- 1)f(x) = √2x3/(x2-x-1)例:以下則不是有理函數:f(x) =√(x2-1)f(x) =√(x-1)/(x+1)f(x) = 1/√(x+1)這些叫做根式函數。有疑問再提出

    2006-01-31 17:16:55 補充:

    若x在√內就不算是rational function嗎..? 是的!

Still have questions? Get your answers by asking now.