In Exercises 1–30, find the domain of each function. g(x) = 3/(x^2-2x-15)

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Welcome back. I'm so glad you're here. We have the function F of X equals eight divided by X squared minus 15, X plus 26 we're asked to find the domain. Well, how do we do that? We look at our function and we ask ourselves if there's anything that could possibly restrict our domain from being all real numbers. And yeah, here there is a fraction. And for the fraction, the denominator cannot equal zero. If we have zero in the denominator it will be undefined. So that X value can't be anything that would make a denominator zero. How do we find out what X values would make the denominator equal to zero? Well, we're going to set the denominator, X squared minus 15. X plus 26 equal to zero. To find out what X values would make it zero. In this case we're going to factor it. So what times what would give us X square? That's going to be X times X. And then what two numbers when multiplied, would give us a positive 26 but would add up to a negative 15. Well in this case that is going to be a minus 13 and a minus two. And because that's equal to zero, there are two factors, we can set each one equal to zero. So X minus 13 equals zero and x minus two equals zero. And now let's add 13 to both sides. For x minus 13 equals zero. We get a value of X equals 13. For x minus two equals zero. Let's add two to both sides. And we get X equals to. What does this mean? That means X equals 13. Or if X equals to we're going to have a zero in our denominator and it's going to be undefined. So for our domain X could be all real numbers except for two and 13 to express that in interval notation, we're going to put a parentheses starting with negative infinity. All the way up to two and then another parentheses to say it can't be too in union with and again, starting with parentheses and starting with that too, Meaning it can be any numbers, not including two, but from two all the way up to and then we go to 13 and put another parentheses, meaning it can't be 13 in union with another parentheses starting with 13. Again, meaning it can be any number after 13 all the way up to positive infinity. Closing with the parentheses again, because we can never quite obtain infinity. We look at our answer choices and this matches with answer choice. C. Well done, we'll catch you on the next one

In Exercises 1–30, find the domain of each function. g(x) = 3/(x^2-2x-15)

Verified Solution

Key Concepts

Domain of a Function

Factoring Quadratic Expressions

Identifying Asymptotes