1. **Problem:** Find $k(9)$, $4k(a)$, and $k(4a)$ for $k(x) = \frac{2}{\sqrt{x - 2a}}$. 2. **Formula:** The function is given by $k(x) = \frac{2}{\sqrt{x - 2a}}$. We will substitute the values into this formula. 3. **Calculate $k(9)$:** $$k(9) = \frac{2}{\sqrt{9 - 2a}}$$ This is the expression for $k(9)$ in terms of $a$. 4. **Calculate $4k(a)$:** First find $k(a)$: $$k(a) = \frac{2}{\sqrt{a - 2a}} = \frac{2}{\sqrt{-a}}$$ Then multiply by 4: $$4k(a) = 4 \times \frac{2}{\sqrt{-a}} = \frac{8}{\sqrt{-a}}$$ Note: This is defined only if $-a > 0$, i.e., $a < 0$. 5. **Calculate $k(4a)$:** $$k(4a) = \frac{2}{\sqrt{4a - 2a}} = \frac{2}{\sqrt{2a}}$$ This is defined if $2a > 0$, i.e., $a > 0$. **Final answers:** - $k(9) = \frac{2}{\sqrt{9 - 2a}}$ - $4k(a) = \frac{8}{\sqrt{-a}}$ (defined if $a < 0$) - $k(4a) = \frac{2}{\sqrt{2a}}$ (defined if $a > 0$)