1. **State the problem:** Laurie's function $f$ takes a word as input and outputs the number of letters in that word. 2. **Given examples:** - $f(\text{banana}) = 6$ because "banana" has 6 letters. 3. **Part (a): Find $f(\text{ned})$** - The word "ned" has 3 letters. - So, $f(\text{ned}) = 3$. 4. **Part (b): Write an input that gives output 5** - We need a word with 5 letters. - Example: "cargo" has 5 letters. - So, $f(\text{cargo}) = 5$. 5. **Part (c): Calculate $f(\text{Tomás}) - 3 \times f(\text{Ava}) + 2 \times [f(\text{Jakub})]^2$** - Count letters in each word: - "Tomás" has 5 letters. - "Ava" has 3 letters. - "Jakub" has 5 letters. - Substitute values: $$f(\text{Tomás}) - 3 \times f(\text{Ava}) + 2 \times [f(\text{Jakub})]^2 = 5 - 3 \times 3 + 2 \times 5^2$$ - Calculate step-by-step: $$= 5 - 9 + 2 \times 25$$ $$= 5 - 9 + 50$$ $$= -4 + 50$$ $$= 46$$ **Final answer:** $46$