1. **State the problem:** We are given two functions: (i) $y = e^{x+1} - 1$ (ii) $f(x) = \frac{x + 2}{x - 1}$ 2. **For (i) $y = e^{x+1} - 1$: Find the value of $y$ for a given $x$ or analyze the function.** The function is an exponential function shifted by 1 in the exponent and then shifted down by 1. 3. **For (ii) $f(x) = \frac{x + 2}{x - 1}$: Analyze the function or find values.** This is a rational function with a vertical asymptote at $x=1$ (denominator zero). 4. **Example: Evaluate (i) at $x=0$: ** $$y = e^{0+1} - 1 = e^1 - 1 = e - 1$$ 5. **Example: Evaluate (ii) at $x=0$: ** $$f(0) = \frac{0 + 2}{0 - 1} = \frac{2}{-1} = -2$$ 6. **Summary:** - The first function is exponential shifted. - The second function is rational with a vertical asymptote at $x=1$. Since the user asked to "Solve this" without specifying what to solve, we interpret it as evaluating or analyzing the functions. Final answers: - For (i) $y = e^{x+1} - 1$ - For (ii) $f(x) = \frac{x + 2}{x - 1}$ No further solving is possible without additional instructions.