profile-img
Vijay posted an Question
April 29, 2021 • 14:05 pm 30 points
  • IIT JAM
  • Mathematics (MA)

Please send the solution to the problem given in the attachment

please send the solution to the problem given in the attachment

3 Answer(s) Answer Now
  • 0 Likes
  • 3 Comments
  • 0 Shares
  • comment-profile-img>
    Aman kumar yadav best-answer

    Have a look.... White line is x^3 and blue line is inverse of x^3 , i.e x ^1/3 .

    cropped-2001330231.jpg
    cropped1634804220.jpg
    cropped-518378761.jpg
    eduncle-logo-app

    doubt

    eduncle-logo-app

    inverse calculate karne k liye variables change kar sakte hai.

    eduncle-logo-app

    agar ni karna chaho to bhi koi problem ni hai. bas last me f-(x) = function of x , me hi likhna.

  • comment-profile-img>
    Deepak singh 1 Best Answer

    inverse of x^3 = x^(1/3) . It will exist or not will depends on Domain .

    cropped3709388431195595008.jpg
    eduncle-logo-app

    what type of inverse is that?

    eduncle-logo-app

    Here I have taken Domain=R to codomain R

    eduncle-logo-app

    if we take domain N (natural no.) and codomain R then inverse not exist

    eduncle-logo-app

    but for inverse only one one condition is sufficient

    eduncle-logo-app

    no , its absolutely incorrect .

    eduncle-logo-app

    there may be some restrictions here ..

    eduncle-logo-app

    Alka ma'am sent me

    eduncle-logo-app

    There may be some restrictions . Ask her to send complete image and then read..

    eduncle-logo-app

    so acc . to you if bijective then inverse exists, right?

    eduncle-logo-app

    yes , see my above counter example .

    eduncle-logo-app

    you say this is absolutely incorrect....ok.... could you plz tell me correct definition of inverse/invertible function

    eduncle-logo-app

    and remember not give any example ....only definition

    eduncle-logo-app

    and one more thing....you say there is some restrictions....so also tell about that restrictions

    eduncle-logo-app

    see , from class 12 NCERT book

    eduncle-logo-app

    if your definition is correct then disprove my above counter example .

    eduncle-logo-app

    you have send , then you will tell restrictions .. send me link from where you found this ... I will check ..

    eduncle-logo-app

    see your NCERT above statement also what they say....if there exist a function g such that gof and fog are identity function

    eduncle-logo-app

    most correct definition of inverse function is this....

    eduncle-logo-app

    your counter example answer

    eduncle-logo-app

    see it's definition in any standard differential calculus book not in NCERT

    eduncle-logo-app

    my definition is for codomain . Your definition is restricted to range . If we restrict codomain to range then we can absolutely say that inverse function exist for restricted function . But what about codomain ?

    eduncle-logo-app

    conclusion is that , 1-1 , onto condition is necessary for function to be invertible . (from your definition also )

whatsapp-btn

Do You Want Better RANK in Your Exam?

Start Your Preparations with Eduncle’s FREE Study Material

  • Updated Syllabus, Paper Pattern & Full Exam Details
  • Sample Theory of Most Important Topic
  • Model Test Paper with Detailed Solutions
  • Last 5 Years Question Papers & Answers