Let `Y = {n^2: n in N} in N`. Consider `f : N ->Y`as `f(n)=n^2`. Show that f is invertible. Find the inverse of f.

Explanation

To show that the function \( f: \mathbb{N} \to Y \) defined by \( f(n) = n^2 \) is invertible, we need to demonstrate that it is both one-to-one (injective) and onto (surjective).

### Step 1: Define the set \( Y \)
The set \( Y \) is defined as:
\[ Y = \{ n^2 : n \in \mathbb{N} \} \]
This means \( Y \) contains all perfect squares of natural numbers, which are \( 1, 4, 9, 16, 25, \ldots \).
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