Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Let f : X → Y be an invertible function. Show that the inverse of f^{ –1} is f, i.e., (f ^{–1} )^{ –1} = f.

Q. 12 Let f : X \rightarrow Y be an invertible function. Show that the inverse of f^{-1} is f, i.e.,
(f^{-1})^{-1} = f

Answers (1)

best_answer

f : X \rightarrow Y

To prove: (f^{-1})^{-1} = f

Let  f:X\rightarrow Y  be a invertible function.

  Then there is    g:Y\rightarrow X  such that   gof =I_x  and fog=I_y

    Also,       f^{-1}= g  

     gof =I_x  and fog=I_y     

   \Rightarrow        f^{-1}of = I_x            and         fof^{-1} = I_y

Hence, f^{-1}:Y\rightarrow X    is invertible function and f is inverse of f^{-1}.

i.e. (f^{-1})^{-1} = f

 

Posted by

seema garhwal

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 Chemistry Exam Analysis 2025: Paper 'moderately difficult' but well balanced
anam-khan

CBSE Class 12 board exam still once a year; 20 lakh expected to appear in 2026 from February 17
anam-khan

CBSE board exams twice a year from 2025-26; 2 subject groups, 'better of two marks' in draft policy

Latest Question