1. **Problem:** Find the value of $x$ such that $h(x) = 2$ where $h(x) = 8 \cdot 2^x$. 2. **Formula:** We use the equation $h(x) = 8 \cdot 2^x = 2$. 3. **Step 1:** Write the equation: $$8 \cdot 2^x = 2$$ 4. **Step 2:** Divide both sides by 8 to isolate $2^x$: $$\cancel{8} \cdot 2^x = \frac{2}{\cancel{8}} \implies 2^x = \frac{1}{4}$$ 5. **Step 3:** Express $\frac{1}{4}$ as a power of 2: $$\frac{1}{4} = 2^{-2}$$ 6. **Step 4:** Equate the exponents since bases are the same: $$x = -2$$ 7. **Step 5:** Check the options: (A) 2, (B) 5, (C) 8, (D) 16. None equals $-2$, so none of the given options satisfy $h(x) = 2$. --- 8. **Problem:** How many points of inflection does the quartic polynomial function $p$ have? 9. **Explanation:** A quartic polynomial can have up to 3 points of inflection. 10. **Answer:** (C) Three --- 11. **Problem:** Find an expression for $f(g(x))$ where $f(x) = e^{2x}$ and $g(x) = \ln(3x)$. 12. **Step 1:** Substitute $g(x)$ into $f$: $$f(g(x)) = e^{2 \cdot g(x)} = e^{2 \ln(3x)}$$ 13. **Step 2:** Use the property $e^{\ln a} = a$: $$e^{2 \ln(3x)} = (e^{\ln(3x)})^2 = (3x)^2 = 9x^2$$ 14. **Answer:** (A) $9x^2$