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Examples finding the domain of functions

Sal shows how to algebraically find the domain of a few different functions.

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  • spunky sam red style avatar for user o1112456
    Isn't the blue equation supposed to be x>7, not x≥7
    (11 votes)
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  • spunky sam blue style avatar for user EmmAnueL
    Why does Sal say "Principal root" instead of square root?
    (4 votes)
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  • male robot hal style avatar for user Yousuf
    the domain of squere root of x-7
    khan said all real values of x such of 7 ≤ x so how can squere root of 7-7 be undefind when its defined as 0 , can someone explain it to me please
    (4 votes)
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  • aqualine ultimate style avatar for user DJ Danvers
    At , why can't x equal 2, and why does it not equal 2? I am sort of confused on how he can to that. Please Advise.
    (3 votes)
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  • blobby green style avatar for user colinjeremiahbernard
    What is a piecewise function?
    (2 votes)
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    • mr pink green style avatar for user David Severin
      A function which varies for different parts of the domain, so the domain is divided into segments, and each segment could have a different function. One of common ones is stair step function with domain 0≤x<1 y=1. 1≤x<2 y=2, 2≤x<3 y=3, etc. which looks like a stair step without the vertical components.
      (3 votes)
  • blobby green style avatar for user Jennifer
    I have a question that involves a triangle: the base is 30 m and is the distance of a camera from a rocket launch pad. The height x increases as the camera's angle is continually adjusted to follow the base of the rocket.
    I've expressed the function as: For the height x at angle theta, the relation R is R = {(theta, x) l (such that) x is the height of the base of the rocket at angle theta}.
    I'm not sure if I've got that right - now I am to give the domain of the function. I think it is probably [0, ...for sure, but could it be [0, infinity)?
    The question also is asking to give the height of the rocket when the elevation angle is pi/3. I have some idea on how to figure this out, but I'm at a loss. I'm taking calculus online and my tutor told be he's too busy b/c he as 160 students.
    I don't know if it's ok for me to post for help on here, but I hope so.
    Thank you.
    (3 votes)
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  • purple pi purple style avatar for user louisaandgreta
    What makes a real number real? How is it different from rational/irrational numbers?
    (2 votes)
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    • area 52 yellow style avatar for user Heraclitus
      Real numbers include rational/irrational numbers, it is just how they are grouped. What makes a real number real, is when it is not complex and also because we say it is. Another reason for we call them real, is because they work in real life. Which is a bad argument, because imaginary numbers are also useful in real life.

      But if you meant real number, as in natural numbers like {1,2,3,4,5...}
      If so, then they are different from irrational numbers because they aren't infinite repeating like 1/7 where it is 0.142857.... and so forth. If we want to compare a natural number to a rational one, it is a rational number. That is just because we can represent it as a natural number always by dividing by 1.
      (2 votes)
  • blobby green style avatar for user Agustín Miranda
    But why isn't he taking in consideration the scenario of x=-5 in the first exercise? Because even though x≠2 it's correct, it doesn't take in consideration that x could be -5, having again an operation where there's a division by zero:

    f(-5)= -5+5/-5-2 = 0/-7
    (1 vote)
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  • boggle purple style avatar for user Tierney
    The last function, h(x) = (x - 5)^2
    x = any number?

    Because I tested several different numbers from negatives to zero to positives and they all worked..
    (1 vote)
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  • female robot grace style avatar for user I.P.
    Hey! Guys! Now, in the first e.g. ( the orange colour one ) x can't be equal to 2 and that's it. But square roots of negative no.s are undefined too, right. So shouldn't the domain also exclude -√ ?
    (1 vote)
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Video transcript

- [Instructor] In this video, we're gonna do a few examples finding domains of functions. So let's say that we have the function f of x is equal to x plus five over x minus two. What is going to be the domain of this function? Pause this video and try to figure that out. All right, now let's do it together. Now the domain is the set of all x values that if we input it into this function, we're going to get a legitimate output. We're going to get a legitimate f of x. And so what's a situation where we would not get a legitimate f of x? Well, if we input an x value that makes this denominator equal to zero, then we're going to divide by zero and that's going to be undefined. And so we could say that the domain, the domain here is all real values of x, such that x minus two does not equal zero. Now typically, people would not want to just see that such that x minus two does not equal zero, and so we can simplify this a little bit so that we just have an x on the left hand side. So if we add two to both sides of this, we would get, actually, let me just do that. Let me add two to both sides. So x minus two not equaling zero is the same thing as x not equaling two, and you could have done that in your head, as well. If you wanted to keep x minus two from being zero, x just can't be equal to two, and so typically, people would say that the domain here is all real values of x such that x does not equal two. Let's do another example. Let's say that we're told that g of x is equal to the principle root of x minus seven. What's the domain in this situation? What's the domain of g of x? Pause the video and try to figure that out. Well, we could say that domain, the domain is going to be all real values of x such that, are we going to have to put any constraints on this? Well when does a principle root function break down? Well if we tried to find the principle root, the square root of a negative number, well, that would then break down, and so x minus seven, whatever we have under the radical here needs to be greater than or equal to zero, so such that x minus seven needs to be greater than or equal to zero. Now another way to say that is if we add seven to both sides of that, that would be saying that x needs to be greater than or equal to seven, so let me just write it that way. So such that x is greater than or equal to seven. So all I did is I said, all right, where could this thing break down? Well, if I get x values where this thing is negative, we're in trouble, so x needs to be greater, x minus seven, whatever we have in this, under the radical needs to be greater than or equal to zero, and so if you say that x minus seven needs to be greater than or equal to zero, you add seven to both sides. You get x needs to be greater than or equal to positive seven. Let's do one last example. Let's say we're told that h of x is equal to x minus five squared. What's the domain here? So let me write this down. The domain is all real values of x. Now are we going to have to constrain this a little bit? Well, is there anything that would cause this to not evaluate to a defined value? Well, we can square any value. To give me any real number and if I square it, I'm gonna just get another real number, and so x minus five can be equal to anything, and so x can be equal to anything. So here, the domain is all real values of x. We didn't have to constrain it in any way like we did the other two. The other two, when you deal with something in the denominator that could be equal to zero, then you've got to make sure that doesn't happen 'cause that would get you an undefined value and similarly, for a radical, you can't take the square root of a negative and so we would, once again, have to constrain on that.