Take it to the limit

Calculus Level 3

Given \(f\left( x \right) = \frac{x + 5}{2}\), \(g\left( x \right) = x + 7\), \(\lim_{x \rightarrow 6}{f\left( g\left( x \right)\right)} = L\) and that \(\lvert f\left( g\left( x \right)\right) - L \rvert < 0.005\), what is the value of \(\delta\) such that \(\lvert x - 6 \rvert < \delta\)?

Detail: all the functions' domains and codomains, in this problem, are the set of the Real Numbers.

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