Let f: R arrow R be defined as f(x)=(2 x-3 π)^3+(4 x)/(3)+ x and...

$$g^{\prime}(f(x))=\frac{1}{f^{\prime}(x)} \Rightarrow g^{\prime}(2 \pi)=\frac{1}{f^{\prime}\left(\frac{3 \pi}{2}\right)}=\frac{1}{\left(\frac{7}{3}\right)}=\frac{3}{7}$$ And \begin{aligned} & g^{\prime \prime}(f(x))=\frac{-f^{\prime \prime}(x)}{\left(f^{\prime}(x)\right)^3} \\ & g^{\prime \prime}(2 \pi)=\frac{-f^{\prime \prime}\left(\frac{3 \pi}{2}\right)}{\left(f^{\prime}\left(\frac{3 \pi}{2}\right)\right)^3}=0 \end{aligned}$$\therefore \quad 7 g^{\prime}(2 \pi)+3 g^{\prime \prime}(2 \pi)=3$$