If \(f(n)=4n^2\) for all n and \(g(n)=n\) if \(n>100\) and \(n^3\) if \(n\le100\), then :

g(n) is of \(O(f(n))\). For all n greater than 100, \(g(n)/f(n)\) \(=n/(4n^2)\) \(=1/(4n)\), which tends to zero. The finitely many smaller inputs do not alter the…