I need some help with the following task:
I should calculate the term $f_1=(\sqrt{2}-1)^6$ therefore I should approximate $\sqrt{2}$ with $1.4$.
I have some other alternative terms
$f_2=(\sqrt{2}+1)^{-6}$, $f_3=(3-2\sqrt{2})^3$ and more but I think these are enough to understand my problem.
First I showed that these term are equivalent.
Then I should calculte the relative condition number and calculate the error and decide which is the best term to use.
I tried to make functions out of the terms
$f_1(x)=(x-1)^6$ so I changed $\sqrt{2}$ to $x$
And then
$$k_{rel}=\frac{f'(x)*x}{f(x)}$$
My Question is should I plug $\sqrt(2)$ or $1.4$ in? And how do I calculate the error?
Thanks for helping !:)