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# Examples finding the domain of functions

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

## Want to join the conversation?

• Isn't the blue equation supposed to be x>7, not x≥7
• It is correct, 7 is a valid solution because √(7-7)=√0=0.
• Why does Sal say "Principal root" instead of square root?
• Square roots have two answers, so if you have sqrt(36) both 6 and -6 are correct answers. The principal root would be the positive number which creates the square root function. The bottom half of the sideways parabola (negative square roots) are not part of the function.
• 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
• The square root of zero is zero because zero times itself is still zero.

So the function you mentioned above is defined for all values of x that are 7 or higher.
• 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.
• You cannot divide by 0, so if x=2, 2-2=0, and the expression becomes indeterminate.
• What is a piecewise function?
• 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.
• 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.
• What makes a real number real? How is it different from rational/irrational numbers?
• 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.
• 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)
• There is a big difference between having the 0 in the denominator as compared to the numerator. In the numerator, 0/-7=0 so you have a value. In the denominator, 5/0 is undefined because you cannot divide by 0.
• 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)
• Yes, the domain of h(x) is all real numbers.