Let f: X → Y be an invertible funct | Class 12 Mathematics Chapter Relations and Functions, Relations and Functions NCERT Solutions

Question:

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

Answer:

Let fX → Y be an invertible function.

Then, there exists a function gY → X such that gof = Ix and fog = Iy

Here, f-1 = g.

Now, gof = Ix and fog = Iy

⇒ f-1of = Iand fof-1=  Iy

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

i.e., (f-1)-1 = f.


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Welcome to the NCERT Solutions for Class 12 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 3 , Question 12: Let f: X → Y be an invertible function. Show that the inverse of f –1 is f, i.e., (f&ndas....