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

**Solution:**

A function is a process or a relation that associates each element 'a' of a non-empty set A, to a single element 'b' of another non-empty set B.

According to the given problem,

Let f : X → Y be an invertible function.

In general, a function is invertible as long as each input features a unique output. That is, every output is paired with exactly one input

Then there exists a function

g : Y → X such that

gof = I_{X} and fog = I_{Y}

Here, f ^{-1} = g

Now,

gof = I_{X} and fog = I_{Y}

⇒ f ^{-}^{1}of = I and fof ^{-}^{1} = I

Hence,

f ^{-}^{1} : Y → X is invertible

and f ^{-1} is f i.e., (f ^{- 1})^{- 1} = f

NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.3 Question 12

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

**Summary:**

Given that f : X → Y be an invertible function. Hence we have shown that the inverse of f^{- 1} is f i.e., (f^{- 1})^{- 1} = f

visual curriculum