Exact solution of generalized inviscid Burgers' equation

Let $f,g:\mathbb{R}\to \mathbb{R}$ be integrable functions, $f$ nowhere zero, and $\varphi (u)=\int du\mathrm{/}f(u)$ be invertible. An exact solution to the generalized nonhomogeneous inviscid Burgers’ equation $u_t+g(u)\mathrm{.}{u}_x=f(u)$ is given, by quadratures.