if $f(x)=||x||_2^2$ for $ x \in \mathbb{R} $, What is the $2-norm$ relative condition number of $f$ with respect to pertubations of x?

What I have tried:

I have tried the following formula from trefethen book page 131-Numerical Linear Algebra.

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I used the 2-norm for: ||J||, ||f(x)||, $||x||$. And my final answer was $\kappa = 2$

My question is. Is this process correct? and how do I know wich norm I have to use for each one of the terms $||J(x)||, ||f(x)|| and ||x||$.

I have these questions because in the same book page 89 and equation (12.3) they state: enter image description here enter image description here

So, I want to know if using the same 2-norm for all the expression is correct and when it is not correct. For instance, in the following example from the same book, page 91 different norms are used.

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