Question: Find (f/g)(x) where $f(x) = \sqrt[3]{4x}$ and $g(x) = 3x + 5$. Include any restrictions on the domain.
1. **State the problem:**
Find the function $\left(\frac{f}{g}\right)(x)$ given $f(x) = \sqrt[3]{4x}$ and $g(x) = 3x + 5$, and determine the domain restrictions.
2. **Recall the formula:**
$$\left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)}$$
3. **Substitute the given functions:**
$$\left(\frac{f}{g}\right)(x) = \frac{\sqrt[3]{4x}}{3x + 5}$$
4. **Determine domain restrictions:**
- The denominator $g(x) = 3x + 5$ cannot be zero because division by zero is undefined.
5. **Solve for restrictions:**
$$3x + 5 \neq 0$$
$$3x \neq -5$$
$$x \neq -\frac{5}{3}$$
6. **Check the numerator:**
- The cube root function $\sqrt[3]{4x}$ is defined for all real $x$, so no restriction from numerator.
7. **Final answer:**
$$\left(\frac{f}{g}\right)(x) = \frac{\sqrt[3]{4x}}{3x + 5}, \quad x \neq -\frac{5}{3}$$
This matches option B.
**Answer: B**