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♡
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
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!
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
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.
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 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.
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.
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 ?
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
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.
A lot of students are asking for a quadratic example. You can find one here:
th-cam.com/video/3PDhq4prArI/w-d-xo.html
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♡
That's TH-cam a world of one example videos that anyone could solve. I guess it makes people feel good to watch :)
@@Greenemath well, definitely not my cup of tea since complex ones often appear on exams🤧
@@yeshik9877 Yes those exams are never easy. Good luck with your studies :)
@@Greenemath oh thanks so much♡ I do need this
You explained much better than any other math teacher trying to explain! Thank you for your help!
Glad to hear the video was helpful!
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
Glad it helped!
😢😂
thank you so much for the algebraic method. my textbook didn’t tell me anything. i needed this so much
You are very welcome. It's usually not covered unless your teacher brings it up.
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!
You are very welcome!
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!
Depending on the function, the algebra can be quite intense. It's a lot easier to use the horizontal line test.
Thank you so much for making this video!! Super helpful for helping me prepare for my upcoming AP Calculus course
You are very welcome.
Just to let y’all know I’m watching this in college to make u feel better lol
I'm surprised your semester is not over. I remember getting out the first week of may.
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?
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
So basically if the function isnt to the second power or |x+a| kind of format than itll be one to one right?
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.
Brilliant explanation. Thank you so much!
Thank you for your kind words, it means a lot to me :)
this is great , you explained better than my prof
Great, glad to hear that.
I am grade 9 and I am supposed to know them; thanks for helping me out!
You are very welcome!
my man you are a live saver
Glad you found the video helpful!
my question is if this could work for x^2, as that isn’t one-to-one yet would still work for this method
Yes, you just need to understand the square root property to go through the math.
Why is he teaching me better than my college professors
It's nice to hear you found the video helpful! 😎
How do I know when I have to put negative signs??
You will have to be more specific. What's the example you are stuck on?
Do limits to +infinity and -infinity apply?
What's the problem you are working on?
@@Greenemath in 1/x, both limits equal 0
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
@@Greenemath in the limit a to +infinity and b to -infinity both functions have the same value, which is 0, though a≠b
@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.
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.
The captions are already in English, which is the native language of the video.
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 ?
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
@@Greenemath okay
this was such a good explanation, thanks!!
You're very welcome!
Very simple explanation...loved it.....THANKS!!!
Glad it was helpful!
Excellent explanation
Glad it was helpful!
Why was an absolute value be necessary? I thought the answer would simply be a+2=b+2 then a=b!
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.
Great explanation. Cheers!
Glad it was helpful!
thx for the help man, keep up the great work :)
Thanks, will do!
Thanks man you helped me a lot
Glad I could help
This was so helpful thank u omg
Glad it helped!
Thanks man,..some good content there
I appreciate that!
Thank you soo much, you really helped me out. :) Please keep it up.
Glad it helped!
Thank u so much, this helped me a loooot
Glad it helped!
Great video!
Glad you enjoyed it
Very helpful, thank you!!
You are very welcome, glad it helped out! :)
"kyooobed". Thanks for the video!
Thanks for watching!
thank you
You are very welcome! :)
Thank you❤️❤️
You’re welcome 😊
Thank you so so much!!
You're welcome!
This is great!
Thanks.
Thank u 🙏🏼
You’re welcome 😊
Brilliant
Great, thanks
Tnx you
You are welcome!