Write the following function in the form \( y=f(u) \) and \( u=g(x) \). Then fin \( y=\left(\frac{x^{2}}{6}+5 x-\frac{4}{x}\right)^{3} \) Write the given function in the form \( y=f(u) \) and \( u=g(x) \). Choose the A. \( y=f(u)=u \) and \( u=g(x)=\frac{x^{2}}{6}+5 x \) B. \( y=f(u)=u \) and \( u=g(x)=\frac{x^{2}}{6}+5 x-\frac{4}{x} \) C. \( y=f(u)=u^{3} \) and \( u=g(x)=\frac{x^{2}}{6}+5 x-\frac{4}{x} \) D. \( y=f(u)=u^{3} \) and \( u=g(x)=\left(\frac{x^{2}}{6}+5 x-\frac{4}{x}\right)^{3} \)

To rewrite the given function \( y=\left(\frac{x^{2}}{6}+5 x-\frac{4}{x}\right)^{3} \) in the form \( y=f(u) \) and \( u=g(x) \), let's analyze the expression. First, the inner function involves an expression that could effectively be grouped together. Therefore, we can define \( u \) as follows: - Let \( u = \frac{x^{2}}{6}+5 x-\frac{4}{x} \). - Then, the function for \( y \) becomes \( y = f(u) = u^{3} \). Based on this breakdown, the correct choice is: C. \( y=f(u)=u^{3} \) and \( u=g(x)=\frac{x^{2}}{6}+5 x-\frac{4}{x} \)