Inverse Functions

[@robintay1449]

Thank you so much! You made inverse functions easier than my professor did.

[@jaineilsart1528]

Finally a channel that teaches quickly and effectivly without any inconvenience.

[@Sureshu583]

Nice one PROFESSORI!!!

[@Cube_Box]

wow, you're so straight forward I understood the whole thing from the thumbnail itself!

[@simplifiedscience7497]

Amazing explanation!! Hats off

[@aprendacompaiva]

Congratulations for the video! Compliments from Brazil

[@theocean6102]

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.

[@leftenanalim]

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

[@olibirdoliver9847]

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

[@DrLiangMath]

Concise and understandable. Excellent!

[@chaynhungkhongkhet833]

Amazing explaination .Thanks sir

[@robertrussell7241]

In the top-right comprehension check, Wouldn't (x+3)/3 simplify to (x/3)+1? This is the same simplification used to get (x/2)+1 in the top left one.

[@pradyumnamishra4810]

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

[@ProfessorDaveExplains]

just turn f(x) into y, then swap x and y. then solve for y. divide by two and then add one.

[@estherntoshya1259]

where did (x/2)+1, come from is it not x+1/2, am lost 😢

[@Tusharplays69]

​@@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

[@davidt9747]

@@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

[@dragonlovesdiamond9512]

⁠@@davidt9747that works too, because (x+2)/2 =y can be simplified to (x/2)+(2/2) aka (x/2) + 1 =y

[@rubinamujahidah1040]

I am in 9th grade but my love for mathematics have brought me here

[@dragonlovesdiamond9512]

does that mean your above or under your grade?

[@Kamal17824]

@@dragonlovesdiamond9512 he's definitely above his grade, usually this is taught between 11th grade - 1st year of uni

[@The_unknown-z2k]

Dang I'm from grade 7, I probably find maths too fascinating

[@Nishantmakadiya]

Only one day absence in school can ruined math after this video all makes sense now thanks

[@ChromeandClean]

Professor , could you please explain the 4th comprehension question , (2x+1)/4, and how you got your answer

[@saramrad7822]

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

[@julianjhulzbayubay1637]

Should change your Comprehension #3 to = x/3 +1. Got confused at it then I used a calc to solve it if it was right (almost got me there lol)

[@mxm14.8k22]

thank you so much professor

[@maximchowdhury6203]

Thanks for this

[@melanietoussaint2130]

Why is important the study of inverse function in the study of function?

[@bh-tabz5134]

Idk

[@0og]

​@@bh-tabz5134why wpuld you answ3r a 2 year old question with "idk"

[@thatomofolo452]

Not really

[@MuntaderAkrem]

Say that there is a shop that offers 30% of the original price , the function will be f(x)=0.7X , where X is the original price and f(x) is the discount price , so now if there is a product costs 28 $ , and we asked ( what was the price of that product before putting the discount ) then we will have to get the inverse function which is f^-1(x)=X/0.7 , plugging the 28 $ into that function and then you'll get 40 $ which is the original price . Hope you get it

[@ryemiranda6800]

​@@MuntaderAkrem Very applicable (not joking)

[@zilog1]

this is interesting because this has to do with my cryptography class for CIT. if a function generates a hash, undo that...

[@mustafasaber5076]

f-¹ (x) = (x + 2) /2 f-¹ (x) = (x + 3)/3 f-¹ (x) = x - 10 f-¹(x) = (2x - 1)/4

[@swxqt6826]

At the end, isn't 1/3(x + 3) simply equal to 1/3x + 1?

[@satbirsingh7269]

thanks sir

[@tGoldenPhoenix]

Done this lesson.

[@science-y9209]

Thank you ❤💙💛💜💓💕💟💗💖

[@wongcheehen-un7dr]

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?

[@thatomofolo452]

It undoes the exponent

[@camxanh2848]

Shouldn't the answer to the first comprehension quest is (x+2)/2? May you check that again?

[@ProfessorDaveExplains]

divide by two first, order of operations

[@camxanh2848]

@@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.

[@medotedo8410]

@@ProfessorDaveExplains both of those algebraic form will yield same value

[@khaledosama1836]

@@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

[@diegomandragora4327]

​@@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! 😊

[@Beingsprout]

Thank you ♡♡♡♡

[@zack_120]

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.

[@kermitthefrog6147]

Why are you angry at the inverse notation looking like an exponent but not at the function notation itself looking like a multiplication?

[@whatdoyouthink2738]

The functions that have square root,they don't have inverse.right?

[@kchrome5796]

The inverse of a square root is a square (^2).

[@medotedo8410]

4:06 undoes ???? undo better

[@deankaraniya7422]

I'd rather not take grammar lessons from someone who avoids using proper punctuation and copula.

[@medotedo8410]

@@deankaraniya7422 Thank you.

[@Mamadvali-02]

❤❤❤

[@How_to_make_a_paper_plane]

Brooo🫡🫡😍🥰

[@science-y9209]

👏👍🌌💐

[@sanchitaagte8215]

absolutely amazing, youre literally doing god's work