How to find domain and range of a rational equation using inverse

👉 Learn how to find the inverse of a rational function. A rational function is a function that has an expression in the numerator and the denominator of the function. The inverse of a function is a function that reverses the "effect" of the original function. One important property of the inverse of a function is that when the inverse of a function is made the argument (input) of a function, the result is x.

Given a function, say f(x), to find the inverse of the function, we first change f(x) to y. Next, we change all x to y and y to x. and then we solve for y. The obtained solution for y is the inverse of the original function.

Timestamps:
0:00 Intro
0:16 Start of Problem

Corrections:
6:19 It's positive 2, not a negative. (x=2)

Organized Videos:
✅ Find the Inverse of a Function
✅ Find the Inverse of a Function | Linear
✅ Find the Inverse of a Function | Rational
✅ Find the Inverse of a Function | Cubic
✅ Find the Inverse of a Function | Quadratic
✅ Find the Inverse of a Function | Cube Root
✅ Find the Inverse of a Function | Square Root
✅ Find the Inverse of a Function | Table
✅ Find the Inverse of a Function | Graph
✅ How to Prove Two Functions are Inverses

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[chrismartin]

isn't it supposed to be, for the range, a positive 2? If you do the same idea to the denominator once you are looking for range, it would be x = 2. If not, why would x -2 still be x = -2 for the range? :"""{

[Junowild]

You made more sense in the first two minutes than my PreCal teacher has all year

[vanessadsouza]

Thank You So much! Our teachers at school just solve the questions and expect us to understand and when we ask questions, they make fun of us. So this was really helpful, thank you

[Jamieforeals]

After 10 years I through myself into a algebra 2 class and I feel like quitting. Too late to drop the class. This is the only channel keeping me alive in this class 👏🏻👏🏻👏🏻when I’m lost I come here 💯

[janahaddad]

thank you so much!! i literally never understood domain and range, in under 7 minutes it all clicked

[Au_Hussar]

I really wish I had you as a teacher many years ago Brian, I'm at university and the tutor/lectures may as well be speaking a different language, you make math make sense.

[igris]

his vids always make us feel like we are sit-in students 😆

[seanjamesongalvin]

Thank you so much, this has been such a big help, especially during quarantine :)

[jasonnwokeji]

Please do not stop posting videos, you explain it far better than my textbooks

[RealAstroWhale]

Thanks sir, this helped, got stumped in finding the range, but now I know

[Fyknite]

Always a great help. Thank you for making these videos

[georgesadler]

Professor McLogan, thank you for an excellent video/lecture on Finding Domain and Range of a Rational Function.

[prastabghimire]

I was in deep trouble and frusted with my life then I just saw your video and it helped and brought me hope . Thank you so much

[TheZmoliver]

Thank you! This is the best example I've seen and I have spent days trying to figure this out. It's like, everyone else seems to be able to skip the 'math' of it in broken down steps. Also, no one else has shown how to flip the variable and solve for the inverse function to find the range.
The crazy part is, this is like chapter 1 in a lot of algebra books! And I can do the rest of the book just fine but domain and range of algebraic functions has always been my achilles heel. Hopefully, not anymore. And I know it's important because I want to get into some calculus soon and that whole subject seems like it's basically full of functions. Thank you again. You're my favorite math tutor on youtube because of your process and just the way you communicate idea. A lot of math teachers aren't always the best with words.

[karldebes]

I am so thankful to have found this video, many of my previous teachers would take much longer to explain this process and I really appreciate your help. You are very good at explaining things in a sensical way!

[aldahirrodriguezsotelo]

I have forgotten this and now have to work with it again and this video put the biggest smile on my face all week!

[bjjtgls]

He who teaches math properly, I hope you're going to have great year, and if you don't, I hope you have the strength to withstand any problem.

[brossa]

You're such a great teacher. Thank you for sharing your knowledge with us

[abnshanag]

I'm from Saudi Arabia this time is first time I watch your videos big thanks for the things you offer, thanks doctor

[philquinz]

Fastest way of finding the range:
Since the degree of both numerator and denominator is the same, just divide the leading coefficient of the numerator which is 2 by the leading coefficient of the denominator which is 1 that will result to 2. Therefore range=(-○○, 2)u(2, ○○).