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Prove that the functions f and g are equal

Source: MTRP 2016 Class 11-Short Answer Type Question: Problem 5 :-

May 31, 2020
functioninjective functionsurjective function

Problem Statement

Let N\mathbb{N} be the set of all positive integers. f,g:N→Nf,g:\mathbb{N} \to \mathbb{N} be funtions such that ff is onto and gg is one-one and f(n)≥g(n)f(n)\geq g(n) for all positive integers nn. Prove that f=gf=g.
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