1. **State the problem:** We need to find the value of the function $b(x) = \sqrt[3]{2x - 1}$ at $x = \frac{9}{2}$. 2. **Recall the formula:** The cube root function is defined as $b(x) = \sqrt[3]{2x - 1}$. 3. **Substitute the value:** Replace $x$ with $\frac{9}{2}$ in the expression: $$b\left(\frac{9}{2}\right) = \sqrt[3]{2 \times \frac{9}{2} - 1}$$ 4. **Simplify inside the cube root:** $$2 \times \frac{9}{2} = \cancel{2} \times \frac{9}{\cancel{2}} = 9$$ So, $$b\left(\frac{9}{2}\right) = \sqrt[3]{9 - 1} = \sqrt[3]{8}$$ 5. **Evaluate the cube root:** $$\sqrt[3]{8} = 2$$ 6. **Final answer:** $$b\left(\frac{9}{2}\right) = 2$$ This means when $x = \frac{9}{2}$, the function $b(x)$ equals 2.