\(f(x)=\frac{5x+2 }{ 3x-5}\) and \(g(x)=x^2-2x-1\)
Substituting, \(f(3)=\frac{(5×3+2)}{(3×3−5)}=\frac{17}{4}\)
\(f(f(3))=\frac{(5×(\frac{17}{4})+2)}{(3×(\frac{17}{4})−5)}=3\)
\(g(f(f(3)))=g(3)=9−6−1=2.\)
\[ f(x) = \left\{ \begin{array}{ll} 1 - 2x & \text{if } x < -1 \\ \frac{1}{3}(7 + 2|x|) & \text{if } -1 \leq x \leq 2 \\ \frac{11}{18} (x-4)(x-5) & \text{if } x > 2 \end{array} \right. \]