In Exercises 76–81, find the domain of each function. g(x) = 4/(x...

Question

In Exercises 76–81, find the domain of each function. g(x) = 4/(x - 7)

Accepted Answer

Welcome back. I'm so glad you're here. We have got a function which is H. Of X equals 11 over X plus six. And we want to find the domain of this function. Well what do we know about? A fraction? We know that the denominator, the number on the bottom cannot equal zero. Otherwise it'll be undefined. So we know that this denominator X plus six cannot equal zero. Well what would make it equal zero? What X value would make it equal zero. We don't know. So we're going to set it equal to zero to find out what that X value would be. That would make it undefined. So let's get X. By itself. We'll subtract six from both sides. So X equals negative six. That is the value that will make our denominator equal zero and therefore undefined. So X. Can be any value in the world other than negative six. How would we write that in interval notation? Well it can be from negative infinity all the way up to negative six but not including negative six. And that will be in union with negative six. All the way up to positive infinity. We look at our answer choices and that's going to match answer choice B. You might be wondering why is it not our answer choice D with this upside down you while the upside down you is going to be the intersection of those numbers where they come together and those two don't come together anywhere. So it's not going to be anything that's the intersection that leaves us with answer choice B. Well done. We'll catch you on the next one.

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