In Exercises 1–8, find the domain of each rational function. f(x)...

Question

In Exercises 1–8, find the domain of each rational function. f(x)=5x/(x−4)

Accepted Answer

consider the given for rational function and fun stuff. Our function is eight x over X -11. So with the rational function we can find this domain by looking for any discontinuities. We will check our discontinuities with our denominator. So if our denominator is equal to zero, we have a dis continuity at that value. Let's go in and take our denominator. Set it equal to zero. So we have X -11 equals to zero. And we can solve To get x equals 11. So we should have this continuity at x equals 11. We can confirm this by plugging it back into our formula and double check. So let's say we take eight times our new value. 11 Over 11 -11. Simplify this 88 at the top of the -11 on the bottom which is zero. Now we have 88/0. This is a dis continuity because we're dividing by zero, which means our domain cannot have the answer. X equals 11. Inside. That's for me. So we can write our domain As all real numbers except for x equals 11. You will say negative infinity Until we get to and 11. All the way to infinity. This ensures that we exclude 11. But keep everything else. If we know that this is our domain, then we should know that our answer is answer. A Okay, I hope you solve the problem. Thank you for watching. Goodbye

Struggling with College Algebra?

In Exercises 1–8, find the domain of each rational function. f(x)=5x/(x−4)

Watch next

Asymptotes practice set