How to Determine if a Function is One-to-One Algebraically

In this lesson, we will learn how to determine if a function is one-to-one algebraically. We already learned that a one-to-one function occurs when for each x, there is only one y and for each y, there is only one x. So now we can use this definition to develop a simple test. If f(a) = f(b), this implies that a = b, if the function is one-to-one. So what we can do is plug in an a for x and plug in a b for x and set these two equal to each other. If it turns out that we end up with a = b, then the function is one-to-one.

[Greenemath]

A lot of students are asking for a quadratic example. You can find one here:

[yeshik]

Omgggg. Finally, a youtuber dealing with complexities rather than dwelling and teaching ONLY BASICS. I mean, it's irritatingly annoying coz all vids that I've been watching was evaluating only linear equations not minding the difficult ones. Anyways, THANKS

[alexa]

needed this for college algebra because my professor didn't explain it as well and THANK YOU SO MUCH

[xffggh]

im literally up at 12 AM rn trying to understand 1-1 functions bc i have an exam tomorrow and i finally understood it after watching ur video, thank u so much you just earned a new subscriber ❤️❤️And i’m so glad i found ur video

[itzamir]

You explained much better than any other math teacher trying to explain! Thank you for your help!

[pieceaisa]

thank you so much for the algebraic method. my textbook didn’t tell me anything. i needed this so much

[devencapritta]

I really liked this video, the current textbook I am using only shows how to determine if a function is one-to-one graphically but not algebraically. Even though the book states that mathematicians also prove a function to be one-to-one algebraically. I was so curious as to how this type of function is shown algebraically, and I was shocked that there was no example of this in my textbook! Again, great video!

[nashonotieno]

Thank you very much, sir, for the good content delivery. I love you and you work. May God bless you.

[joshsalmon]

I think the holdup for me was that I didn't understand that I could replace the X's with A and B! Thank you!

[rychick]

Thank you so much for making this video!! Super helpful for helping me prepare for my upcoming AP Calculus course

[jacquelinegoetz]

Brilliant explanation. Thank you so much!

[moji]

this is great, you explained better than my prof

[michelissa]

I am grade 9 and I am supposed to know them; thanks for helping me out!

[MaryamTea]

this was such a good explanation, thanks!!

[amd]

how about sinx? sin(a)=sin(b)
a=b
but we know from the graph thats false?
so what are the limits of this way of verifying?

[estifmarley]

o thnx very much i like u method and you teaching absolute values are not one to one function but u don't teaching like log, exponential, power function please in next video teach us ?

[nicolelang]

If you could go into the settings for this video and change the auto-generated captions language to English (United States) - rather than Vietnamese - that would be really useful! I can't use your video for my students because I need good captions.

[ProofDetectives]

Asslam o alikum. Thank you for the video. Have a good day.

[monkeymarlena]

my question is if this could work for x^2, as that isn’t one-to-one yet would still work for this method

[Customs]

Why was an absolute value be necessary? I thought the answer would simply be a+2=b+2 then a=b!