The functions \( f, g \), and \( h \) are defined as follows. \[ f(x)=|-10+9 x| \quad g(x)=\frac{8+x^{3}}{x^{3}} \quad h(x)=\sqrt{-6-5 x} \] Find \( f\left(-\frac{2}{3}\right), g(4) \), and \( h(-4) \). Simplify your answers as much as possible. \[ \begin{array}{r}\left(-\frac{2}{3}\right)=\square \\ h(4)=\square\end{array} \]

To compute the values of the functions at the specified inputs, let's evaluate each function step-by-step. **Calculating \( f\left(-\frac{2}{3}\right) \)**: \[ f(x) = |-10 + 9x| \] Substituting \( x = -\frac{2}{3} \): \[ f\left(-\frac{2}{3}\right) = |-10 + 9\left(-\frac{2}{3}\right)| \] \[ = |-10 - 6| = |-16| = 16 \] **Calculating \( g(4) \)**: \[ g(x) = \frac{8 + x^3}{x^3} \] Substituting \( x = 4 \): \[ g(4) = \frac{8 + 4^3}{4^3} \] \[ = \frac{8 + 64}{64} = \frac{72}{64} = \frac{9}{8} \] **Calculating \( h(-4) \)**: \[ h(x) = \sqrt{-6 - 5x} \] Substituting \( x = -4 \): \[ h(-4) = \sqrt{-6 - 5(-4)} \] \[ = \sqrt{-6 + 20} = \sqrt{14} \] Thus, the results are: \[ \begin{array}{r} f\left(-\frac{2}{3}\right) = 16 \\ g(4) = \frac{9}{8} \\ h(-4) = \sqrt{14} \end{array} \]