The functions \( f, g \), and \( h \) are defined as follows. \[ f(x)=\frac{x^{3}+12}{x^{3}} \quad g(x)=|-10+4 x| \quad h(x)=\sqrt{1+5 x} \] Find \( f(-3), g\left(-\frac{3}{2}\right) \), and \( h(2) \). Simplify your answers as much as possible. \( g\left(-\frac{3}{2}\right)=\square \)

To find \( f(-3) \), we substitute \(-3\) into the function \( f(x) \): \[ f(-3) = \frac{(-3)^{3} + 12}{(-3)^{3}} = \frac{-27 + 12}{-27} = \frac{-15}{-27} = \frac{15}{27} = \frac{5}{9}. \] Next, we calculate \( g\left(-\frac{3}{2}\right) \): \[ g\left(-\frac{3}{2}\right) = \left|-10 + 4 \left(-\frac{3}{2}\right)\right| = \left|-10 - 6\right| = \left|-16\right| = 16. \] Finally, we evaluate \( h(2) \): \[ h(2) = \sqrt{1 + 5 \cdot 2} = \sqrt{1 + 10} = \sqrt{11}. \] So, summarizing our results: \[ f(-3) = \frac{5}{9}, \quad g\left(-\frac{3}{2}\right) = 16, \quad h(2) = \sqrt{11}. \] Thus, \( g\left(-\frac{3}{2}\right) = 16 \).