This is the same problem as an earlier example, but we're going to solve it a different way. Since c = 4, f(c) = 8. Saying we want f(x) to be within ε of 8
means we want to have
7.5 < f(x) < 8.5,
or
7.5 < 2x < 8.5.
We can solve this inequality in one step: divide through by 2 to find
3.75 < x < 4.25. Now, subtract 4 from all parts of the inequality:
3.75  4 < x  4 < 4.25  4
0.25 < x  4 < 0.25.
This means x must be within 0.25 of 4, therefore δ = 4.
