y=sqrt(x), why y IS a function of x?

y is funtion of x
因為你put一個數入x就只能出一個y

sqrt(25) = 5
但係唔等於 -5
- sqrt(25) = -5
唔等於5

sqrt(x)只能表示正數
係唔可能出到負數

2007-01-08 08:34:39 補充：
myisland8132依位人兄你就錯y=sqrt(x)只可以係正數y=-sqrt(x)先係負數條curve兩條curve組合埋一齊先可以出到你幅圖,亦即係y^2 = x所以唔係人地個software能力有限,係你個software有問題y=sqrt(x)只屬於above x軸條curve 係唔包下面架有時書本既model answer未必一定岩,又或者係typing mistake請唔好見到個answer就照住黎吹如果個model answer話1 + 1 = 3唔通你又話岩在下並無冒犯之意,只係指出錯處

2007-01-09 12:18:31 補充：
下面位人兄有冇讀過pure math呀你知唔知function既definition係乜呀唔識就返學校問老師或者自己買參考書睇啦你問下老師y = √x 同 y = ±√x 有冇分別如果佢話有既,咁我冇野好講我只可以話比你聽y = ±√x係等於y^2 = x仲有√25 = 5 or -5 係絕對唔正確佢only表示√25 = 5係唔可以= -5如果我地寫 x =√25 跟住只可以寫 = 5但係如果x^2 = 25, 咁我地就可以話 x = 5 or -5我咁講都係希望令發問者明白依件事同埋希望杜絕你依d謬論

補充得好正~

I assume you have certain level of mathematical analysis background to ask whether sqrt() is a function or not. The simple answer is rooted at how you define a function.

The usual definition for a function is to be well defined so that one value in a domain maps to exactly one value in its range. That is a secondary level definition.

A multi-valued function can be a function that map each value in its domain to one or more values in its range. In this sense, you can say that sqrt() is a multi-valued function. If you can always choose one of the multiple value in the multiple values mapped in a function as principal value, the value is called principal value. A function that always return the principal value of a multi-valued function is called the principle branch of the function. For example, the sqrtp() function that always return positive value of sqrt() is the principle branch of sqrt(). Another example are arcsin()/arccos()... functions, these functions always return value between -pi to +pi as principle value.

In this sense, there is two ways that sqrt() is a function, either because it is a multi-valued function, or sqrt() is implicitly understood as the principle branch of sqrt() and therefore a function.

The material are obtained from a complex analysis book, although there is nothing complex here.

我唔知對唔對...
我之前聽過一個講法
當我地設 x 為任意數都有 y 值
但好明顯當 x < 0, y 係無答案的
而且 y^2 = x
才 y = √x or - √x
而直接 y = √x 係唔會有負值
所以個program無錯 model ans都無錯
如果我第一個講法是對的

上面個位人兄係答錯佐啦
個model answer 都話y isn't the function of x
點解y不是function
因為function的定義是每一個x值只能對應一個y值
現在
y=sqrt(x)
則 y=sqrt(25)= 5 or -5
有兩個x值對應﹐所以y不是function
I still don't know why y won't have two values in this case.
y是有兩個值呀
model answer 個句
"drawing graph software" will not produce the curve below 0
係話個software能力有限only
真正的graph 會係0甘

圖片參考：http://www.maa.org/cvm//1998/01/ucfg/article/images/X2-Inv.gif

好明顯一個x值對應兩個y值


2007-01-08 01:20:18 補充：
x是負數﹐y冇對應數是對的但係個句子應該是"drawing graph software" will not produce the curve of the left hand side of 0不是 below of 0吧所以我唯有理解成個software能力有限only

2007-01-09 08:19:38 補充：
上面個位﹐若果就0甘y=sqrt(x)都係函數﹐0甘仲有乜野唔係函數你話我照住個model answer 吹水﹐0甘你0米又係照住個大題目why y IS a function of x 去答但係你有冇留意到人地係題目到又有寫 y is a not function of x. (it's true)即係佢自己都唔sure is or not

2007-01-09 08:20:03 補充：
因為人地已經post佐個model answer 話係not﹐0甘正路係係解釋點解會係not﹐但係你就解釋到成個model answer wrong 0甘﹐所以我0米話你答錯而且事實上就算y=sqrt(x)係function﹐亦只係因為硬寫明 y的值域是正數而唔係因為一寫y=sqrt(x) 個y就一定是正數的

2007-01-09 08:24:17 補充：
我現在諗番起個0的software就真係會以為y=sqrt(x) 個y就一定是正數的 我終於明啦其實sqrt(25)= 5 or -5 絕對正確﹐我寫成篇文就係要令到個發問者明白li件事only

2007-01-09 08:27:20 補充：
以上只係表明個人立場﹐并冇任何攻擊含意﹐敬希垂注

2007-01-09 08:47:22 補充：
原來佢寫 sqr(y)=x, y is a not function of x. (it's true)0甘當我4,5兩行係廢話雖然我都唔係好agree﹐又冇寫明邊個係自變數﹐邊個係因變數你話係唔係andrew