Question

The domain of the real-valued function
\[ f(x) = \sqrt{\frac{2x^2 - 7x + 5}{3x^2 - 5x - 2}} \] is:

• A. \( (-\infty, -\frac{1}{3}) \cup [1,2) \cup [\frac{5}{2}, \infty) \)
• B. \( (-\infty, 1) \cup (2, \infty) \)
• C. \( (-\frac{1}{3}, \frac{5}{2}) \)
• D. \( (-\infty, -\frac{1}{3}] \cup [\frac{5}{2}, \infty) \)

Hint:

For rational functions inside a square root, ensure the numerator is non-negative while avoiding zeros of the denominator.