1. The problem asks to find the exact value of $k(9)$ given the piecewise function: $$k(x) = \begin{cases} x^2 & \text{if } x < 5 \\ x + 2 & \text{if } x = 5 \\ 2 - x & \text{if } x > 5 \end{cases}$$ 2. To solve this, we need to determine which part of the piecewise function applies when $x=9$. 3. Since $9 > 5$, we use the third case: $k(x) = 2 - x$. 4. Substitute $x=9$ into the expression: $$k(9) = 2 - 9$$ 5. Simplify the expression: $$k(9) = -7$$ 6. Therefore, the exact value of $k(9)$ is $-7$.