1. **Stating the problem:** Given the relation $$I = 1 + \frac{u}{f}$$ (a) Make $f$ the subject of the relation. (b) Find $I$ when $u = 5$ and $f = 4$. --- 2. **Formula and rules:** The relation is $$I = 1 + \frac{u}{f}$$ where $I$, $u$, and $f$ are variables. To make $f$ the subject, isolate $f$ on one side of the equation. --- 3. **Step-by-step solution for (a):** - Start with $$I = 1 + \frac{u}{f}$$ - Subtract 1 from both sides: $$I - 1 = \frac{u}{f}$$ - Multiply both sides by $f$ to eliminate the denominator: $$f (I - 1) = u$$ - Divide both sides by $(I - 1)$ to isolate $f$: $$f = \frac{u}{I - 1}$$ So, the subject $f$ is: $$f = \frac{u}{I - 1}$$ --- 4. **Step-by-step solution for (b):** - Given $u = 5$, $f = 4$, find $I$ using the original formula: $$I = 1 + \frac{u}{f} = 1 + \frac{5}{4}$$ - Calculate the fraction: $$\frac{5}{4} = 1.25$$ - Add 1: $$I = 1 + 1.25 = 2.25$$ --- **Final answers:** (a) $$f = \frac{u}{I - 1}$$ (b) $$I = 2.25$$