There is a linked-list with $n$ elements, which are $x_1,x_2,\ldots,x_n$. Let $f(n)$ be the time complexity of inserting a new element $x_{n+1}$ to the tail of the list, and $g(n)$ be that of deleting the last element $x_n$. If there is only one pointer pointed to the head of the list, we know to access the list is time-consuming, and functions $f(n)$ and $g(n)$ are denoted as $f_1(n)$ and $g_1(n)$ in this case. To improve it, we may also add another pointer pointed to the tail of it, so the functions $f(n)$ and $g(n)$ become $f_2(n)$ and $g_2(n)$. Which of the following option is false if $n$ becomes large.