How to Find the Inverse of a Rational Function

In this video we will go over a step by step process for finding the inverse of a rational function. The function is f(x) = (2x - 3)/(x + 1) and we find the inverse function f^(-1)(x). I hope this helps someone who is learning algebra and studying inverse functions.

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Thank you:)

[NattyPi]

watching this for support. Just passed my 5 week Diiff eq course with 100%. We used the same book so I posted your play list in our class discord and everyone wanted to say thank you. the class was async so we enjoyed the lectures Step-professor lol

[ninaschust]

This brings back memories from over 20 years ago. Thank you for sharing.

[chaosredefined]

y = (2x-3)/(x+1)
Note that -3 = 2-5.
y = (2x+2-5)/(x+1)
Split the numerator into 2x+2 and -5
y = (2x+2)/(x+1) - 5/(x+1)
Cancel (x+1) from each term in the first fraction on the RHS
y = 2 - 5/(x+1)
Add 5/(x+1) - y to both sides
5/(x+1) = 2-y
Take the inverse of both sides
(x+1)/5 = 1/(2-y)
Multiply both sides by 5
x+1 = 5/(2-y)
Subtract 1 from both sides. I will write the 1 on the RHE as (2-y)/(2-y)
x = 5/(2-y) - (2-y)/(2-y)
Combine fractions
x = (5 - 2 + y)/(2-y)
x = (3+y)/(2-y)

So f^(-1)(x) = (3+x)/(2-x).

No need to confuse yourself about the xy or anything like that.

[ananyasharma]

Sir please do a q and a I really want to know about you..

[heferh]

Math Sorcerer help me my neighbors are doing a loud party, it's 4:56 am

[cynthiastandley]

Can you suggest a practical example of where finding the inverse would be useful? TIA

[kareemakram]

How to know if the function is bijective to have a defined inverse

[dreed]

Peanut gallery: you are multiplying both sides by (y+1)/1 but omitted the 1 denominator and used the term "cancel" when you are really multiplying by the reciprocal.

[oQuAdShto]

Kinda felt like a variation of implicit differentiation

[sasimulasyon]

this is the subject of high school 2 in turkey

[gvi]

I love these information videos but they are far too long. Anyway to condense this into 2 minutes?