Question

The domain of the function \[ \sqrt{2x - 5x^2 + 6} + \sqrt{2x + 8 - x^2} \] is:

• A. \( [2, 3] \)
• B. \( [-2, 1] \cup [3, 4] \)
• C. \( [-2, 1] \)
• D. None of these

Hint:

The domain of a function with square roots is restricted by the values that make the expression inside the square roots non-negative.

Answer 1

The Correct Option is C

The domain of the function is determined by the values of \( x \) for which both square roots are defined. After solving, the valid range for \( x \) is \( [-2, 1] \).

Step 2: Conclusion.
Thus, the correct answer is \( [-2, 1] \).