1. **State the problem:** We are given the function $$f(x) = \sqrt{\frac{x+2}{x-2}}$$ and need to find the value(s) of $$x$$ such that $$f(x) = 3$$. 2. **Set up the equation:** Substitute $$f(x) = 3$$ into the function: $$3 = \sqrt{\frac{x+2}{x-2}}$$ 3. **Square both sides** to eliminate the square root: $$3^2 = \frac{x+2}{x-2}$$ $$9 = \frac{x+2}{x-2}$$ 4. **Solve for $$x$$:** Multiply both sides by $$x-2$$: $$9(x-2) = x+2$$ $$9x - 18 = x + 2$$ 5. **Bring all terms to one side:** $$9x - x = 2 + 18$$ $$8x = 20$$ 6. **Divide both sides by 8:** $$x = \frac{20}{8} = \frac{5}{2} = 2.5$$ 7. **Check the domain:** The denominator $$x-2$$ cannot be zero, so $$x \neq 2$$. Our solution $$x=2.5$$ is valid. **Final answer:** $$x = 2.5$$