1. The problem states: Given the function $f(x) = 7x^3 + 5x - 6$, find $\frac{4}{f(x)}$. 2. The function $f(x)$ is a cubic polynomial: $f(x) = 7x^3 + 5x - 6$. 3. To find $\frac{4}{f(x)}$, we simply write: $$\frac{4}{f(x)} = \frac{4}{7x^3 + 5x - 6}$$ 4. This expression cannot be simplified further without specific values for $x$. 5. Therefore, the final answer is: $$\frac{4}{7x^3 + 5x - 6}$$