Q.10 Let f : X \rightarrow Ybe an invertible function. Show that f has a unique inverse.
(Hint: suppose g_1 and g_2 are two inverses of f. Then for all y \in Y,
fog_1 (y) = I_Y (y) = fog_2 (y). Use one-one ness of f).

Answers (1)

Let f : X \rightarrow Ybe an invertible function

Also, suppose f has two inverse g_1 and g_2

For y \in Y, we have

     fog_1(y) = I_y(y)=fog_2(y)

 \Rightarrow     f(g_1(y))=f(g_2(y))  

\Rightarrow             g_1(y)=g_2(y)                     [f is invertible implies f is one - one]

\Rightarrow                     g_1=g_2                        [g is one-one]

Thus,f has a unique inverse.

Preparation Products

Knockout NEET May 2021 (One Month)

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

₹ 14000/- ₹ 6999/-
Buy Now
Foundation 2021 Class 10th Maths

Master Maths with "Foundation course for class 10th" -AI Enabled Personalized Coaching -200+ Video lectures -Chapter-wise tests.

₹ 999/- ₹ 499/-
Buy Now
Foundation 2021 Class 9th Maths

Master Maths with "Foundation course for class 9th" -AI Enabled Personalized Coaching -200+ Video lectures -Chapter-wise tests.

₹ 999/- ₹ 499/-
Buy Now
Knockout JEE Main April 2021 (One Month)

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

₹ 14000/- ₹ 6999/-
Buy Now
Knockout NEET May 2021

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

₹ 22999/- ₹ 14999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions