Inverse Functions
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- Опубліковано 9 лис 2017
- We know about functions, so what are inverse functions? Let's find out!
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Thank you so much! You made inverse functions easier than my professor did.
Finally a channel that teaches quickly and effectivly without any inconvenience.
Nice one PROFESSORI!!!
wow, you're so straight forward I understood the whole thing from the thumbnail itself!
Amazing explanation!! Hats off
Congratulations for the video!
Compliments from Brazil
Amazing explaination .Thanks sir
Thanks for this
Concise and understandable. Excellent!
The one thing I just don't understand is when in your example of x+2 and x-2 (when x =3) that the 5 you get from adding 3 and 2 can just be substituted back into x-2 like this (5-2) to obtain the 3 when this 5 is a y value.
I am in 9th grade but my love for mathematics have brought me here
Only one day absence in school can ruined math after this video all makes sense now thanks
Thank you ♡♡♡♡
Done this lesson.
What about the squared of a negative number? The reverse operation should return back a negative number. So sqrt could should return either a positive or negative value
Square function does not have its inverse function because its not a one on one function and it wont be a function after it is inversed
Thank you ❤💙💛💜💓💕💟💗💖
this is interesting because this has to do with my cryptography class for CIT. if a function generates a hash, undo that...
thanks sir
At the end, isn't 1/3(x + 3) simply equal to 1/3x + 1?
It undoes the exponent
Why is important the study of inverse function in the study of function?
Idk
@@bh-tabz5134why wpuld you answ3r a 2 year old question with "idk"
Not really
Maybe he/she meant real world applications
But I have tried with with multivariable functions (e. g( x^2 / 7)+( 3(x^2))/5 ) and end up getting some y=uy with looped functions is it normal?
Sir , in the first comprehension ...how did you solve ...when (x-1) is in the brackets . I mean what to subtract from both sides ...I didn't get it ...I don't get it when there are brackets
just turn f(x) into y, then swap x and y. then solve for y. divide by two and then add one.
where did (x/2)+1, come from is it not x+1/2, am lost 😢
@@estherntoshya1259i guess you've already found the reason but if in case you didn't, lemme clarify it for you.
f(x)=2(x-1)
Now, let f(x)=y
y=2(x-1)
swap the variables for f-¹(x).
x=2(y-1)
Divide by 2
x/2=y-1
Since you're adding 1 after you have already created a fraction x/2, you've to add it to the whole fraction. Thus,
(x/2)+1=y
f-¹(x)=(x/2)+1
@@Tusharplays69 thanks, but for some reason when i see x=2(y-1), the most reasonoble thing seems to be x=2y-2, then y=(x+2)/2
Professor , could you please explain the 4th comprehension question , (2x+1)/4, and how you got your answer
firstly you swap the x by y so y=2x+1/4 then x=2y+1/4 after that it's 4x=2y+1 so y=4x-1/2 and this is the inversed function's answer. I Hope that u could understand
Shouldn't the answer to the first comprehension quest is (x+2)/2? May you check that again?
divide by two first, order of operations
@@ProfessorDaveExplains Ah now I see. Both "(x+2)/2" and "x/2 + 1" are the same thing. "x/2 + 1" can also be written as "x/2 + 2/2", hence expressed as "(x + 2)/2" since the two fractions have the same denominator. Btw, thank you for making these quality content. It really helps me out.
@@ProfessorDaveExplains both of those algebraic form will yield same value
@@camxanh2848
The second comprehension quest could be also expressed as "x/3 + 1" but for some reason it was left in the form of "x+3/3" unlike the first quest. I don't know why
@@ProfessorDaveExplains Expanding the bracket first and then do everything else works too( - won't break the rules of bidmas- ), and it directly leads to X+2/2. Which is actually equivalent to the answer displayed in the video. Only that it's a more compact algebraic fraction.
Ps; Thanks for the fantastic content, and educating the world! 😊
The functions that have square root,they don't have inverse.right?
The inverse of a square root is a square (^2).
Brooo🫡🫡😍🥰
👏👍🌌💐
absolutely amazing, youre literally doing god's work
4:06 undoes ???? undo better
I'd rather not take grammar lessons from someone who avoids using proper punctuation and copula.
@@deankaraniya7422 Thank you.
3:46 - The notation is chaotic. originally y=4x-5, and then it becomes y=(x+5)/4 !? How do you reconcile this obvious contra/error? Mathematicians should've come up with a better way to express inverse functions. Just like the inverse trig function where e.g. the inverse of sin(x) = arcsin(x), this UNAMBIGUOUSLY separate the two reciprocal functions.
0:40, f^-1 is the original notation for 1/f, e.g. 10^(-1)=1/10=0.1. why then here you subjectively disqualify the rule? This is not correct even it is used as such. This is one of the reasons why some math subjects are 'hard' to understand and misleading.
Why are you angry at the inverse notation looking like an exponent but not at the function notation itself looking like a multiplication?