1. **State the problem:** We need to find the domain of the function $$f(x) = 2x^2 + 5\sqrt{x - 2}$$. 2. **Recall the domain rule for square roots:** The expression inside the square root must be greater than or equal to zero because the square root of a negative number is not a real number. 3. **Set the radicand condition:** $$x - 2 \geq 0$$ 4. **Solve the inequality:** $$x \geq 2$$ 5. **Interpret the result:** The domain of $$f(x)$$ is all real numbers $$x$$ such that $$x$$ is greater than or equal to 2. **Final answer:** The domain for $$f(x)$$ is all real numbers **greater** than or equal to 2.