I was reading the below link of math.stackexchange. The question is about to solve the limit of a function Limit of a given function
The function is: \begin{equation} f(x) = \lim_{n \to \infty}{(2\sqrt[n]x-1)^n} \end{equation} where $x \in R$ and $x \ge 1$
As per my understanding,the limit of the function should be 1 but it's given $x^2$ in the above link.
Here is my understanding:
when $n \to \infty$, $\sqrt[n]x \to 1$ and $(2\sqrt[n]x-1) \to 1$.
So the limit of the funciton f(x) will also approach to $1$ when $n \to \infty$.
Can anyone explain where I am wrong.