Here's my problem. Here's what I tried:

$\displaystyle |f(x)-3| < 0.6$ whenever $\displaystyle 0 < |x-5| < \delta$

$\displaystyle |f(x)-3| < 0.6 = -0.6 < f(x)-3 < 0.6 = 2.4 < f(x) < 3.6$

The graph tells me that $\displaystyle 2.4 < f(x) < 3.6$ when $\displaystyle 4 < x < 5.7$

What I'm not completely sure about is what to do from here.

I think delta is 0.7, but I'm not sure how to conclude that mathematically.

Is this problem asking to find the smallest value of delta that the limit of f(x) at x is less then 0.6 away from 3?