1. **Problem Statement:** Find the range of the function $$f(x) = \frac{2x+1}{x-1}$$. 2. **Recall:** The range of a function is the set of all possible output values (values of $f(x)$). 3. **Step 1: Identify domain restrictions.** The function is undefined where the denominator is zero, i.e., at $x=1$. 4. **Step 2: Express $y = f(x)$ and solve for $x$.** $$y = \frac{2x+1}{x-1}$$ Multiply both sides by $(x-1)$: $$y(x-1) = 2x + 1$$ $$yx - y = 2x + 1$$ 5. **Step 3: Rearrange to isolate $x$.** $$yx - 2x = y + 1$$ $$x(y - 2) = y + 1$$ $$x = \frac{y + 1}{y - 2}$$ 6. **Step 4: Determine values of $y$ for which $x$ is undefined.** The expression for $x$ is undefined when the denominator is zero: $$y - 2 = 0 \implies y = 2$$ 7. **Step 5: Conclusion:** The function $f(x)$ can take all real values except $y=2$. **Therefore, the range of $f$ is $$\mathbb{R} - \{2\}$$.** **Answer: (c) $$\mathbb{R} - \{2\}$$**