Name: 関数の領域 (Domain of a function)
Uploaded: 2021-01-14T05:33:21.000Z
Duration: 9 min 59 s

命令形

Welcome to my presentation on domain of a function.

関数の定義域のビデオへようこそ。

頻度を表す副詞

The domain of a function, you'll often hear it combined

多くの場合、関数の定義域と値域は

But the domain of a function is just what values can I put into

関数の定義域は関数に入れることができる値です。

Let's say I had f of x is equal to, let's say, x squared.

それでは、例を行いましょう。

What values of x can I put in here so I get a valid

Well, I can really put anything in here, any real number.

ここに置くことがでるx の値は

So here I'll say that the domain is the set of x's

x の 2乗が得られる値は、何ですか。

such that x is a member of the real numbers.

任意の実数置くことができます。

So this is just a fancy way of saying that OK, this r with

this kind of double backbone here, that just means real

numbers, and I think you're familiar with real numbers now.

That's pretty much every number outside of the complex numbers.

And if you don't know what complex numbers

実数に精通していると思います。

You probably won't need to know it right now.

The real numbers are every number that most people are

familiar with, including irrational numbers, including

今知っている必要はありません。

transcendental numbers, including fractions -- every

実数は、ほとんどの皆さん馴染みの数で

So the domain here is x -- x just has to be a member

And this little backwards looking e or something, this

just means x is a member of the real numbers.

So let's do another one in a slight variation.

e の後ろ向きのようにみえるもの

So let's say I had f of x is equal to 1 over x squared.

これが、 x が実数と示します。

Can I still put any x value in here and get

f （x ）＝１／x＾２とします。

x 値に、どんな数字を入れても

合理的な答えが得られますか？

I don't know what it is, so this is undefined.

No one ever took the trouble to define what 1 over 0 should be.

And they probably didn't do, so some people probably thought

about what should be, but they probably couldn't find out with

a good definition for 1 over 0 that's consistent with

１／０を定義することはできません。

考える人もいるかも知れませんが

So we can't put 0 in and get a valid answer for f of 0.

So here we say the domain is equal to -- do little brackets,

that shows kind of the set of what x's apply.

That's those little curly brackets, I didn't

１／０は未定義のままになります。

だから f （0 ）は未定義です。

x is a member of the real numbers still, such that

０では、有効な答えを取得することはできません。

So here I just made a slight variation on what I had before.

Before we said when f of x is equal to x squared that x

Now we're saying that x is any real number except for 0.

This is just a fancy way of saying it, and then these curly

かつ、x が 0 に等しくないです。

前の例から、わずかに変化しました。

Let's say f of x is equal to the square root of x minus 3.

So up here we said, well this function isn't defined when we

ここでは、x は、0 以外の任意の実数です。

But what's interesting about this function?

Can we take a square root of a negative number?

Well until we learn about imaginary and complex

f（x）がx−３ の平方根に等しいとしましょう。

この関数が定義されていない場合は

So here we say well, any x is valid here except for the x's

that make this expression under the radical sign negative.

しかし、この関数は興味深いですね。

So we have to say that x minus 3 has to be greater than or

負の数の平方根を取ることができますか？

equal to 0, right, because you could have the square to 0,

虚数と複素数について学ぶまで

この場合、答えは得られません。

So x minus 3 has to be greater than or equal to 0, so x has to

この式が負になる数を除いたものです。

So here our domain is x is a member of the real numbers,

such that x is greater than or equal to 3.

平方根をとるために必要です、

What if I said f of x is equal to the square root of the

x−３を０以上とする必要があります。

So now it's getting a little bit more complicated.

Well just like this time around, this expression of

the radical still has to be greater than or equal to 0.

So you can just say that the absolute value of x minus 3 is

f（x）が、（｜x｜−３）の平方根では

So we have the absolute value of x has to be greater

And if order for the absolute value of something to be

greater than or equal to something, then that means that

やはり、 0 以上の必要があります。

x has to be less than or equal to negative 3, or x has to be

It makes sense because x can't be negative 2, right?

Because negative 2 has an absolute value less than 3.

３以上であることが必要です。

It has to be further in the negative direction than

negative 3, or it has to be further in the positive

So, once again, x has to be less than negative 3 or x

X が−２では、成り立ちません。いいですか？

has to be greater than 3, so we have our domain.

−２では、その絶対値が3 未満です。

So we have it as x is a member of the reals

だから x を−３より小さく する必要があります。

さらに負の方向にする必要があります。

−３以下、あるいは３以上です。