$$ \begin{align} f(x) &= x^ 3 + 3 x + 1 \g(x) &= \frac{ 3 }{x} \h(x) &= \int_{0}^{x} \sin(t) dt \i(x) &= L_{\delta}= \left\{\begin{matrix} \frac{1}{2}(y - \hat{y})^{2} & if \left | (y - \hat{y}) \right | < \delta\ \delta ((y - \hat{y}) - \frac1 2 \delta) & otherwise \end{matrix}\right. \end{align} $$