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)

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

 

Preparation Products

JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Rank Booster NEET 2021

This course will help student to be better prepared and study in the right direction for NEET..

₹ 13999/- ₹ 9999/-
Buy Now
Knockout JEE Main April 2021 (Subscription)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 4999/-
Buy Now
Knockout JEE Main April 2022 (Subscription)

Knockout JEE Main April 2022 Subscription.

₹ 5499/-
Buy Now
Knockout NEET May 2021 (Subscription)

An exhaustive E-learning program for the complete preparation of NEET..

₹ 4999/-
Buy Now
Exams
Articles
Questions