1. **Problem Statement:** Find values of $x$, if any, at which the functions are not continuous. 2. **Function 11:** $f(x) = 5x^4 - 3x + 7$ - This is a polynomial function. - Polynomials are continuous everywhere on $\mathbb{R}$. - Therefore, $f(x)$ is continuous for all real $x$. 3. **Function 12:** $f(x) = \sqrt[3]{x - 8}$ - The cube root function $\sqrt[3]{x}$ is continuous everywhere. - Since $f(x)$ is a composition of continuous functions (cube root and linear function $x-8$), it is continuous everywhere. 4. **Conclusion:** - For function 11, there are no values of $x$ where $f$ is not continuous. - For function 12, there are no values of $x$ where $f$ is not continuous. **Final answer:** Both functions are continuous for all real numbers, so no discontinuities exist.