Algebra

Domain of a function | Functions and their graphs | Algebra II | Khan Academy

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Welcome to the presentation on the field of mathematical function What is the domain? The field of the mathematical function, and you may have heard of the term in combination Domain and domain But the field of the mathematical function is the values \u200b\u200bthat I can put in Mathematical function and get the right result So let’s start with some examples Suppose I have f (x) = x ^ 2 f (x) = x ^ 2 So let me ask you What are the x values \u200b\u200bthat we can put here and get An output that achieves x ^ 2? Well, I could put any number here, any real number So I can say here that the field is a set of x Like x belongs to the real numbers So you could say well here, this r is with These are the two important parts, that is Real numbers, and I think the real numbers are familiar for you now It is any number except for complex numbers And if you don’t know what the complex numbers are this is good Because you probably won’t need to know it now The real numbers are every familiar number for people The relative numbers include VIR, and include Sublimation numbers, including fractions — all The numbers are real numbers So the field here is x – x should belong For the real numbers set And these are the background parts that resemble e or anything, this That is, x belongs to the real set of numbers So let’s solve another example that is a little bit different We will solve another slightly different example So suppose I have f (x) = 1 / x ^ 2 Do we follow the same thing? Can i still put the value of x here and get A convincing answer? Well what is the product of (f (0)? . f (0) = 1/0 How much is the output 1/0? I don’t know what it is, so it isn’t defined Not defined Many tried to find an outcome of 0/0 But they couldn’t, so some people would think Its equal, but they could not find Good definition of 1/0 and this is constant In mathematics So 1/0 remains unknown Thus f (0) is not defined So we can’t put 0 in parentheses and get a correct answer for f (0) So we say here that the field = – we put some brackets So we show the group to which x belongs These two brackets I did not stay Draw them well x belongs to the real set of numbers, plus that x is not equal to 0 So here I made a change from what I had previously done Before we say when f (x) = x ^ 2, that is x It is any real number Now we can say that x is any real number except 0 This method is fictitious, and these two brackets They mean the group Let’s solve more examples Let’s say (f) x = the square root of x – 3 So as I said above, well this math function is not known when The denominator is 0 But what is so interesting about this mathematical function? Can we take the square root of a negative number? Well if we had not learned the complex and imaginary numbers We cannot So here we say OK, meaning x is right here except for the value of x That makes the statement inside the root code negative So we have to say that x – 3 must be greater than or Equal to 0, right? Because we can have a square of 0 It’s simple, it’s 0 So x x 3 must be greater than or equal to 0, so the value of x must To be greater than or equal to 3 So the field here is x belongs to the real numbers Such as x is greater than or equal to 3 . Let us now solve a difficult example What if (f (x = square root)? For | x – 3 | Now here is some kind of complication Well, just like this time, this phrase The root is still greater than or equal to 0 So you could say that | x – 3 | Greater than or equal to 0 So we have | x | It should be bigger From or equal to 0 And until the absolute value of a value Greater than or equal to a number, this means that x must be less than or equal to -3, or x Greater than or equal to 3 This is logical because x cannot equal -2, right? Because -2 has an absolute value less than 3 So x must be less than -3 And you will be in the negative direction further than -3, or in the positive direction After positive 3 So again, x must be less than -3 or Greater than 3, so we get the field We got it x image belongs to the real numbers I always forget Is this the line? I forgot whether it was a column or a line It has been many years since I solved it Examples like this But anyway, I think you understood the principle Any real number will be here, as long as x is less From -3, less than or equal to -3, or x Greater than or equal to 3 Let me ask a question now What if instead of this – it was the maqam This is the isolated issue here So we now have 1 / square root | x – 3 | So how has this situation changed? This phrase is not just in the denominator This is not just what must be greater than or equal to 0, could it be 0? Well, no, because then we’re going to get the square value of 0 It is 0 and we will have the denominator 0 So this issue appears to be in addition to this The issue goes hand in hand So now when we have 1 / square root of | x – 3 |, it is no longer greater than or equal to 0, or even greater than 0, right? It is greater than 0 Because we cannot have 0 in the denominator If it is greater than 0, then we say greater than 3 We will get rid of this sign of equality Let me erase it well . It’s a little different color, but maybe You did not notice this Let’s Begin Actually we have to solve another example as long as we have more time . Let me erase this OK Now f (x) = 2, if x is an even number And 1 / (x – 2) (x -1), if x is an odd number So what’s the area here? What value of x is it appropriate to put here? We have two conditions here If x is an even number, we will use this condition, then (f (4 – okay) This is equal to 2 because we used this Ø condition for here But this condition applies when x is an odd number As we did in the last example, what are they? Where this is invalidated? Well, when the denominator is 0 Well the denominator is 0 when x = 2, or x = 1, correct? But this condition only applies when x is an odd number So x = 2 does not apply in this condition So x = 1 only is what can be applied to the condition So the field here is x belongs to the real numbers, where is x is not equal to 1 I think the time is up Enjoy solving these field problems .

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