**Q: Find the domain of the function:**

**d(x) = √(x-1)/(x-6)**

A: To find the domain (which is what values x can be), think of what values **x cannot be**.

The two problem areas we have are (1) a square-root and (2) a denominator.

(1) Anything in under a square-root must be positive (greater than or equal to zero)… This is because we cannot take a square-root of a negative number.

So, (x – 1) ≥ 0

x – 1 ≥ 0

x ≥ 1

x must be greater than or equal to 1.

(2) The denominator can never equal zero. So,

(x – 6) ≠ 0

x ≠ 6

Now, we must put the two answers together: x must be greater than or equal to 1, but cannot be 6.

In interval notation, this is: [1, 6) U (6, ∞).

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Oh my gosh. You are such a lifesaver. Has anyone told you that? Well I’m saying it right now. My teacher doesn’t explain anything well at all. She comes up with weird examples that make no sense then gets mad at us when we try to figure it out on our own. SO THANK YOU SO MUCH. It’s all so simplified and makes much more sense now!

I just have one question, and it’s probably a bit obvious. But what does the U mean in the interval notation bit?

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Kaitlyn,

Thank you for the compliments. Ask questions any time. I really do love to help.

Good question you have, because I didn’t clearly explain. The “U” stands for “union”. It is just formal notation to join the two intervals together. For example, (1, 3) U (3, 5) means you can go from 1 to 3, jump over 3, then go from 3 to 5. Basically saying numbers 1-5 but skipping 3. Does that make more sense?

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Yes that makes so much more sense now! Thank you so much Stacey. c:

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