1. **Stating the problem:** We are given the function $$f(x) = \frac{1}{\sqrt{2x - 1}}$$ and need to analyze its domain and behavior. 2. **Formula and rules:** The function involves a square root in the denominator. For the function to be defined: - The expression inside the square root must be positive: $$2x - 1 > 0$$ - The denominator cannot be zero, so $$\sqrt{2x - 1} \neq 0$$ which means $$2x - 1 \neq 0$$ 3. **Find the domain:** - Solve $$2x - 1 > 0$$ $$2x > 1$$ $$x > \frac{1}{2}$$ - Since the denominator cannot be zero, $$x \neq \frac{1}{2}$$ but this is already excluded by the strict inequality. 4. **Domain conclusion:** The domain of $$f$$ is $$\left(\frac{1}{2}, +\infty\right)$$. 5. **Summary:** - The function $$f(x) = \frac{1}{\sqrt{2x - 1}}$$ is defined only for $$x > \frac{1}{2}$$. - For values of $$x$$ less than or equal to $$\frac{1}{2}$$, the function is not defined because the square root would be of a negative number or zero in the denominator. **Final answer:** $$\boxed{\text{Domain of } f = \left(\frac{1}{2}, +\infty\right)}$$