1. **State the problem:** Find the value of $f(0)$ and find $x$ such that $f(x) = -5$ for the function $f : x \to \frac{1}{2}x - 1$. 2. **Formula and rules:** The function is given by $f(x) = \frac{1}{2}x - 1$. To find $f(0)$, substitute $x=0$ into the function. To find $x$ for which $f(x) = -5$, solve the equation $\frac{1}{2}x - 1 = -5$. 3. **Calculate $f(0)$:** $$f(0) = \frac{1}{2} \times 0 - 1 = 0 - 1 = -1$$ 4. **Solve for $x$ when $f(x) = -5$:** Start with: $$\frac{1}{2}x - 1 = -5$$ Add 1 to both sides: $$\frac{1}{2}x = -5 + 1 = -4$$ Multiply both sides by 2: $$x = -4 \times 2 = -8$$ 5. **Final answers:** - $f(0) = -1$ - $x = -8$ when $f(x) = -5$