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.

Let's calculate each function step by step: 1. For \( f(-3) \): \[ f(-3) = \frac{(-3)^{3} + 12}{(-3)^{3}} = \frac{-27 + 12}{-27} = \frac{-15}{-27} = \frac{15}{27} = \frac{5}{9} \] 2. For \( g\left(-\frac{3}{2}\right) \): \[ g\left(-\frac{3}{2}\right) = \left|-10 + 4\left(-\frac{3}{2}\right)\right| = \left|-10 - 6\right| = \left|-16\right| = 16 \] 3. For \( h(2) \): \[ h(2) = \sqrt{1 + 5(2)} = \sqrt{1 + 10} = \sqrt{11} \] Thus, the calculated values are: - \( f(-3) = \frac{5}{9} \) - \( g\left(-\frac{3}{2}\right) = 16 \) - \( h(2) = \sqrt{11} \)