Let $f,g:(0,\infty)\to\mathbb{R}$ be defined by $f(x)=\int_{-x}^{x}\big(|t|-t^{2}\big)e^{-t^{2}}\,dt,\qquad g(x)=\int_{0}^{x^{2}} t^{1/2}e^{-t}\,dt.$ Then the value of $g\!\left( f\!\big(\sqrt{\log_e 9}\,\big)+g\!\big(\sqrt{\log_e 9}\,\big)\right)$ is: