**Title: Understanding Inverse Functions through Set-Builder Notation****Introduction:**Consider the function \( f = \{(n, n^2 - 1) \} \) such that \( n < 5 \) and \( n \in \mathbb{N} \), written in set-builder notation, which defines a set containing a list of ordered pairs.---**Objective:**Write the inverse of \( f \) as a set in list form containing ordered pairs.**Options:**1. \( f^{-1} = \{(0,1), (3,2), (8,3), (15,4)\} \)2. \( f^{-1} = \{(0, -1), (1,0), (2,3), (3,8), (4,15)\} \)3. \( f^{-1} = \{(1,0), (2,3), (3,8), (4,15)\} \)4. \( f^{-1} = \{(-1,0), (0,1), (3,2), (8,3), (15,4)\} \)5. \( f^{-1} = \{(3,2), (8,3), (15,4)\} \)---**Explanation:**To find the correct inverse of the function \( f \), we begin by identifying the original set of ordered pairs from the function \( f \). The function \( f \) is defined as:\[ f = \{(n, n^2 - 1) \mid n < 5, n \in \mathbb{N}\} \]Here \( \mathbb{N} \) represents the set of natural numbers.As per the definition, we need to identify the elements \( (n, n^2 - 1) \) for \( n = 1, 2, 3, 4 \):1. For \( n = 1 \): \( (1, 1^2 - 1) = (1, 0) \)2. For \( n = 2 \): \( (2, 2^2 - 1) = (2, 3) \)3. For \( n = 3 \): \( (3, 3^2 - 1) = (3

consider the function f={(n,n^2-1) such that n<5,n€N}. written in set builder notation,which…

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Consider the function f= {(n,n² –1) such that n<5,n€N}, written in set-builder notation, which defines a set containing a list of ordered pairs. Write the inverse of f as a set in list form containing ordered pairs.