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Determining whether values are in domain of function

Sal shows how to test whether or not a value is or isn't in the domain of a function.

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• why @ principal square root of -9 is not in domain but the same kind of answer square root 6 is in the domain. *Why?*
• There is no principal square root of negative numbers in the real domain. Taking the square root of negative numbers goes into the imaginary domain. When we are talking domain and range, we limit it to real numbers.
• How do you know whether or not something is in the domain or not?
• For each number that you want to know whether or not it is in the domain, you plug in that number for x, and see if the answer makes sense.

I'm going to look at the function x+5/x-3

If I plug in 0, I get 0+5/0-3, which turns into -5/3. That's a real number, so 0 is in the domain of the function.

If I plug in 3, I get 3+5/3-3, which turns into 8/0. You can't really divide by zero, so 8/0 is not a real number, and 3 is not in the domain of the function.

Hope that helps :)
• is there a shortcut i can use?
• you could always remember that the denominator of a fraction can't equal to 0.
For example, if f(x)=x/x+1 x can be anything but -1

You can't have a square root of a negative number.
For example, if f(x)=√ x then x has to be a positive number

So if you check the denominator of fraction and the √ x that would make the process of finding the domain faster!
• Wait a minute, how is 0/8 a proper number but 8/0 is not? i thought 0/8 was the bad number in fractions :P
and
• You can't divided a number by zero. So 8/0 or any number divided by 0 is undefined.
• How do I tell if a function is undefined or not?
• If any number is divided by zero including zero, it is undefined.
• How do I know if something is legitimate or not? What does he mean when he says that?
• can any negative number like -8,-9 could be in domain
• It depends on the function. Some functions can have literally any number in them, while others can only have very specific numbers. A Function with a square root in it for instance can't have ANY negative numbers in it.
• Did not understand what the function means, how to find the domain and the non-domain