Functions $$\(\mathrm{f}\)$$ and $$\(\mathrm{g}\)$$ are defined for $$\(x \in \mathbb{R}\)$$ by $$\[ \begin{aligned} &\mathrm{f}: x \mapsto \frac{1}{2} x-a, \\ &\mathrm{~g}: x \mapsto 3 x+b, \end{aligned} \]$$ where $$\(a\)$$ and $$\(b\)$$ are constants. Given that $$\(\mathrm{gg}(2)=10\)$$ and $$\(\mathrm{f}^{-1}(2)=14\)$$, find the values of $$\(a\)$$ and $$\(b\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

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