Function Evaluation D05416

1. **State the problem:** We are given the function $$f(x) = \frac{x + 5}{2}$$ and need to evaluate it for different inputs: $$-1$$, $$44$$, $$z - 5$$, and $$5z$$. 2. **Formula used:** The function is defined as $$f(x) = \frac{x + 5}{2}$$. To evaluate $$f(a)$$ for any input $$a$$, substitute $$x$$ with $$a$$ and simplify. 3. **Evaluate each part:** (a) Evaluate $$f(-1)$$: $$f(-1) = \frac{-1 + 5}{2} = \frac{4}{2} = 2$$ (b) Evaluate $$f(44)$$: $$f(44) = \frac{44 + 5}{2} = \frac{49}{2}$$ Simplify if possible: $$\frac{49}{2}$$ is already simplified. (c) Evaluate $$f(z - 5)$$: $$f(z - 5) = \frac{(z - 5) + 5}{2} = \frac{z - 5 + 5}{2} = \frac{z}{2}$$ (d) Evaluate $$f(5z)$$: $$f(5z) = \frac{5z + 5}{2} = \frac{5(z + 1)}{2}$$ 4. **Summary of answers:** - (a) $$2$$ - (b) $$\frac{49}{2}$$ - (c) $$\frac{z}{2}$$ - (d) $$\frac{5(z + 1)}{2}$$