Given the functions: \[ f(x)=x^{3}+7 x \quad g(x)=\sqrt{3 x} \quad h(x)=5 x+7 \] Evaluate the function \( h(f(x)) \) for \( x=2 \). Write your answer in exact simplified form. Select "Undefined" if applicable.

To evaluate the function \( h(f(x)) \) for \( x=2 \), we first need to find \( f(2) \) and then substitute that value into \( h \). 1. Calculate \( f(2) \): \[ f(x) = x^3 + 7x \] \[ f(2) = 2^3 + 7 \cdot 2 = 8 + 14 = 22 \] 2. Now, use this result in the function \( h(x) \): \[ h(x) = 5x + 7 \] \[ h(f(2)) = h(22) = 5 \cdot 22 + 7 = 110 + 7 = 117 \] Thus, the value of \( h(f(2)) \) is \( \boxed{117} \).