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

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  • เผยแพร่เมื่อ 26 ม.ค. 2025

ความคิดเห็น • 95

  • @Greenemath
    @Greenemath  ปีที่แล้ว +6

    A lot of students are asking for a quadratic example. You can find one here:
    th-cam.com/video/3PDhq4prArI/w-d-xo.html

  • @yeshik9877
    @yeshik9877 4 ปีที่แล้ว +61

    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 SOOOOOOO MUUUUUCH♡

    • @Greenemath
      @Greenemath  4 ปีที่แล้ว +4

      That's TH-cam a world of one example videos that anyone could solve. I guess it makes people feel good to watch :)

    • @yeshik9877
      @yeshik9877 4 ปีที่แล้ว +5

      @@Greenemath well, definitely not my cup of tea since complex ones often appear on exams🤧

    • @Greenemath
      @Greenemath  4 ปีที่แล้ว +3

      @@yeshik9877 Yes those exams are never easy. Good luck with your studies :)

    • @yeshik9877
      @yeshik9877 4 ปีที่แล้ว +2

      @@Greenemath oh thanks so much♡ I do need this

  • @itzamir3518
    @itzamir3518 2 ปีที่แล้ว +4

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

    • @Greenemath
      @Greenemath  2 ปีที่แล้ว

      Glad to hear the video was helpful!

  • @xffggh
    @xffggh ปีที่แล้ว +4

    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

  • @pieceaisa5046
    @pieceaisa5046 ปีที่แล้ว +2

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

    • @Greenemath
      @Greenemath  ปีที่แล้ว

      You are very welcome. It's usually not covered unless your teacher brings it up.

  • @joshsalmon4523
    @joshsalmon4523 ปีที่แล้ว +2

    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!

    • @Greenemath
      @Greenemath  ปีที่แล้ว

      You are very welcome!

  • @devencapritta6827
    @devencapritta6827 ปีที่แล้ว +2

    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!

    • @Greenemath
      @Greenemath  ปีที่แล้ว +1

      Depending on the function, the algebra can be quite intense. It's a lot easier to use the horizontal line test.

  • @rychick5684
    @rychick5684 5 หลายเดือนก่อน +1

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

    • @Greenemath
      @Greenemath  5 หลายเดือนก่อน +1

      You are very welcome.

  • @Alyssa-wx3kx
    @Alyssa-wx3kx 3 ปีที่แล้ว +5

    Just to let y’all know I’m watching this in college to make u feel better lol

    • @Greenemath
      @Greenemath  3 ปีที่แล้ว

      I'm surprised your semester is not over. I remember getting out the first week of may.

  • @amd8668
    @amd8668 3 ปีที่แล้ว +2

    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?

    • @Greenemath
      @Greenemath  3 ปีที่แล้ว +1

      f(x) = sin(x) is not a one-to-one function. We can make it a one-to-one function by restricting the domain.
      f(x) = sin(x), -π/2 ≤ x ≤ π/2
      This allows us to have the same range from [-1, 1]
      You can watch this video, which covers the subject in much more detail:
      th-cam.com/video/vmOx0Ngzg0Y/w-d-xo.html
      or from our free website:
      www.greenemath.com/Trigonometry/25/Inverse-Circular-FunctionsLesson.html
      www.greenemath.com/Trigonometry/25/Inverse-Circular-Functions.html

  • @dean6978
    @dean6978 3 ปีที่แล้ว +2

    So basically if the function isnt to the second power or |x+a| kind of format than itll be one to one right?

    • @Greenemath
      @Greenemath  3 ปีที่แล้ว +1

      To determine if a function is one-to-one, generally you want to graph things and use the horizontal line test. The algebraic method is something teachers use to test your algebraic skills. There will be many functions that aren't one-to-one that don't involve a second power or absolute value. For example, f(x) = sin x, is not a one-to-one function.

  • @jacquelinegoetz9391
    @jacquelinegoetz9391 4 ปีที่แล้ว +6

    Brilliant explanation. Thank you so much!

    • @Greenemath
      @Greenemath  4 ปีที่แล้ว

      Thank you for your kind words, it means a lot to me :)

  • @moji0858
    @moji0858 ปีที่แล้ว +1

    this is great , you explained better than my prof

    • @Greenemath
      @Greenemath  ปีที่แล้ว

      Great, glad to hear that.

  • @michelissa9388
    @michelissa9388 4 ปีที่แล้ว +6

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

    • @Greenemath
      @Greenemath  4 ปีที่แล้ว

      You are very welcome!

  • @qussayalmutairi1695
    @qussayalmutairi1695 3 ปีที่แล้ว +2

    my man you are a live saver

    • @Greenemath
      @Greenemath  3 ปีที่แล้ว

      Glad you found the video helpful!

  • @monkeymarlena4210
    @monkeymarlena4210 2 ปีที่แล้ว +1

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

    • @Greenemath
      @Greenemath  2 ปีที่แล้ว

      Yes, you just need to understand the square root property to go through the math.

  • @galaxyghost1340
    @galaxyghost1340 3 ปีที่แล้ว +1

    Why is he teaching me better than my college professors

    • @Greenemath
      @Greenemath  3 ปีที่แล้ว

      It's nice to hear you found the video helpful! 😎

  • @babushka1098
    @babushka1098 9 หลายเดือนก่อน

    How do I know when I have to put negative signs??

    • @Greenemath
      @Greenemath  9 หลายเดือนก่อน

      You will have to be more specific. What's the example you are stuck on?

  • @thegrefgfake5482
    @thegrefgfake5482 8 หลายเดือนก่อน

    Do limits to +infinity and -infinity apply?

    • @Greenemath
      @Greenemath  8 หลายเดือนก่อน

      What's the problem you are working on?

    • @thegrefgfake5482
      @thegrefgfake5482 8 หลายเดือนก่อน

      @@Greenemath in 1/x, both limits equal 0

    • @Greenemath
      @Greenemath  8 หลายเดือนก่อน

      f(x) = 1/x is a one-to-one function using our definition from the lesson.
      if f(a) = f(b) this implies that a = b
      f(a) = 1/a
      f(b) = 1/b
      1/a = 1/b
      a = b, so the function is one-to-one

    • @thegrefgfake5482
      @thegrefgfake5482 8 หลายเดือนก่อน

      @@Greenemath in the limit a to +infinity and b to -infinity both functions have the same value, which is 0, though a≠b

    • @Greenemath
      @Greenemath  8 หลายเดือนก่อน

      @thegrefgfake5482 f(x) = 1/x can never ever be zero. For a fraction to be zero the numerator needs to be zero and the denominator needs to not be zero. Here, the numerator is 1, which can never be zero.

  • @nicolelang3849
    @nicolelang3849 3 ปีที่แล้ว +1

    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.

    • @Greenemath
      @Greenemath  3 ปีที่แล้ว +1

      The captions are already in English, which is the native language of the video.

  • @estifmarley15
    @estifmarley15 4 ปีที่แล้ว +2

    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 ?

    • @Greenemath
      @Greenemath  4 ปีที่แล้ว +1

      If you watch the full playlist, you will find what you are looking for. Check out our channel page for the college algebra playlist. You need to start watching at around video 100 and keep going. We cover logs and exponential functions. You can also use the practice tests for free on GreeneMath.com/College_Algebra.html

    • @estifmarley15
      @estifmarley15 4 ปีที่แล้ว

      @@Greenemath okay

  • @MaryamTea
    @MaryamTea 4 ปีที่แล้ว +2

    this was such a good explanation, thanks!!

    • @Greenemath
      @Greenemath  4 ปีที่แล้ว

      You're very welcome!

  • @parthkadam8669
    @parthkadam8669 2 ปีที่แล้ว +1

    Very simple explanation...loved it.....THANKS!!!

    • @Greenemath
      @Greenemath  2 ปีที่แล้ว

      Glad it was helpful!

  • @kaushikramr100
    @kaushikramr100 3 ปีที่แล้ว +1

    Excellent explanation

    • @Greenemath
      @Greenemath  3 ปีที่แล้ว

      Glad it was helpful!

  • @Customs07
    @Customs07 2 ปีที่แล้ว +1

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

    • @Greenemath
      @Greenemath  2 ปีที่แล้ว

      The point of the exercise is to show algebraically that the absolute value function is not a one-to-one function. You can do this graphically using the horizontal line test if that's what you prefer.
      Recall with an absolute value such as:
      |ax + b| = |cx + d|
      We need to solve:
      ax + b = cx + d
      But also
      -(ax + b) = cx + d
      In your example you missed one of the scenarios, you need to consider how absolute value works. It flips a negative into a positive.

  • @mattkriese7170
    @mattkriese7170 ปีที่แล้ว +1

    Great explanation. Cheers!

    • @Greenemath
      @Greenemath  ปีที่แล้ว

      Glad it was helpful!

  • @michaelherrera338
    @michaelherrera338 3 ปีที่แล้ว +1

    thx for the help man, keep up the great work :)

    • @Greenemath
      @Greenemath  3 ปีที่แล้ว

      Thanks, will do!

  • @jizzbunker6974
    @jizzbunker6974 3 ปีที่แล้ว +1

    Thanks man you helped me a lot

    • @Greenemath
      @Greenemath  3 ปีที่แล้ว

      Glad I could help

  • @mariaikas9641
    @mariaikas9641 ปีที่แล้ว +1

    This was so helpful thank u omg

  • @ivanschege194
    @ivanschege194 4 ปีที่แล้ว +1

    Thanks man,..some good content there

    • @Greenemath
      @Greenemath  4 ปีที่แล้ว

      I appreciate that!

  • @johnboyca9434
    @johnboyca9434 4 ปีที่แล้ว +1

    Thank you soo much, you really helped me out. :) Please keep it up.

  • @linamulugeta5514
    @linamulugeta5514 3 ปีที่แล้ว +1

    Thank u so much, this helped me a loooot

  • @gabewebb_
    @gabewebb_ ปีที่แล้ว +1

    Great video!

    • @Greenemath
      @Greenemath  ปีที่แล้ว

      Glad you enjoyed it

  • @SP-ge6kv
    @SP-ge6kv 4 ปีที่แล้ว +1

    Very helpful, thank you!!

    • @Greenemath
      @Greenemath  4 ปีที่แล้ว

      You are very welcome, glad it helped out! :)

  • @syzygonal
    @syzygonal 2 ปีที่แล้ว +1

    "kyooobed". Thanks for the video!

    • @Greenemath
      @Greenemath  2 ปีที่แล้ว

      Thanks for watching!

  • @olaayman1900
    @olaayman1900 4 ปีที่แล้ว +1

    thank you

    • @Greenemath
      @Greenemath  4 ปีที่แล้ว +1

      You are very welcome! :)

  • @mostafaekbal3863
    @mostafaekbal3863 3 ปีที่แล้ว +1

    Thank you❤️❤️

    • @Greenemath
      @Greenemath  3 ปีที่แล้ว

      You’re welcome 😊

  • @kidistdawit4734
    @kidistdawit4734 4 ปีที่แล้ว +1

    Thank you so so much!!

  • @rezanasser6236
    @rezanasser6236 2 ปีที่แล้ว +1

    This is great!

  • @r.793
    @r.793 3 ปีที่แล้ว +1

    Thank u 🙏🏼

    • @Greenemath
      @Greenemath  3 ปีที่แล้ว

      You’re welcome 😊

  • @AlbertChanda-oy9m
    @AlbertChanda-oy9m ปีที่แล้ว +1

    Brilliant

  • @hilinak
    @hilinak 4 ปีที่แล้ว +1

    Tnx you

    • @Greenemath
      @Greenemath  4 ปีที่แล้ว

      You are welcome!