Given $\epsilon=0.01$ and $a=2$. Find a value $\delta$ corresponding to the given value of $\epsilon$ so that the definition of continuity is satisfied.

I supposed, that since $f(x)=f(a)+\epsilon$, we could solve the equation $$f(x)-f(a)=\epsilon$$$$\sqrt{x}-\sqrt{2}=0.01/-0.01$$

for $x$, choose the smallest $x$, then find the $\delta$ that is sufficiently small, so the change in the value of the function remains within $0.01$. Why doesn't this method work? The correct answer is $2\epsilon$.