Find the domain of each rational expression. (x + 3) / (x - 6)...

Question

Find the domain of each rational expression. (x + 3) / (x - 6)

Accepted Answer

Hey everyone welcome back for the following rational expression. Were asked to solve for the domain were given X-plus eight divided by X -24. Alright, so let's go ahead and label this equation? We're going to call this F. Of X. That's going to be a rational expression And it's X-plus eight divided by X -24. Now when we have a rational expression, okay, we're dividing one function by another function. What we wanna do is first look at the domain of each of those functions individually. Okay. The domain of the numerator and the domain of the denominator. Our function F is going only going to exist at points where both of those exist. Okay, so let's look at the domain of each of those individually. So the domain of X plus eight. Well this is a linear equation. It's a polynomial of degree one. When we have a polynomial, we know that the domain is gonna be from negative infinity to positive infinity. So this linear function, we can choose any X value, plug it into this function and we're going to get a corresponding y value out of it. Okay. Alright, so let's do the same for the denominator. So the domain Of X - and this is also going to be from negative infinity to positive infinity. This is another linear equation. A polynomial of degree one. So it's the exact same. Alright, so we know that our numerator and denominator exists for every X value. So we're not going to run into an issue there? Where else could we have issues. Okay, where else could our function not be defined? Well we're dividing by something. Okay. We know that we can't divide by zero. So if our denominator, X -24 is equal to zero, then our function f is going to be undefined. So half of X is undefined When X -24 is equal to zero. Okay, so we want to figure out what X value that happens at and exclude that from our domain X -24 is equal to zero. This happens when X is equal to 24. Okay. And so that's going to be excluded from our domain. So when we write the domain of f. Okay, we're gonna have The points from negative infinity all the way up to 24 but we're gonna use a round bracket to indicate that we don't include the point at 24. And then we're gonna join this with the interval from 24 all the way up to infinity. So what we've done is we've used the interval from negative infinity all the way to positive infinity. And we've just excluded the point when we are exactly at x equals 24. Alright, so the domain is going to be the Union of the two intervals. The first from negative infinity to 20 for the second from 24 to infinity. OK. Where all the endpoints are not included? So if we look at the answer choices, we see that this is going to correspond with answer C. That's it for this one. Thanks everyone for watching. See you in the next video.

Find the domain of each rational expression. (x + 3) / (x - 6)

Key Concepts

Rational Expressions

Domain of a Function

Finding Restrictions on the Domain

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