Advertisement Remove all ads

Let F: X → Y Be an Invertible Function. Show that the Inverse Of F−1 Is F, I.E., (F−1)−1 = F. - Mathematics

Let fX → Y be an invertible function. Show that the inverse of f−1 is f, i.e., (f−1)−1 = f.

Advertisement Remove all ads

Solution

Let fX → Y be an invertible function.

Then, there exists a function gY → X such that gof = IXand fo= IY.

Here, f−1 = g.

Now, gof = IXand fo= IY

⇒ f−1of = IXand fof−1= IY

Hence, f−1Y → X is invertible and f is the inverse of f−1

i.e., (f−1)−1 = f.

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

NCERT Class 12 Maths
Chapter 1 Relations and Functions
Q 12 | Page 19
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×