Question

The domain of the function \(f(x) = \sqrt{x - \sqrt{1 - x^2\) is:}

• A. [-1, -\frac{1}{\sqrt{2}}] \cup [\frac{1}{\sqrt{2}}, 1]
• B. [-1, 1]
• C. (-\infty, -\frac{1}{\sqrt{2}}] \cup [\frac{1}{\sqrt{2}}, +\infty]
• D. [\frac{1}{\sqrt{2}}, 1]

Hint:

Be extremely careful when squaring inequalities! Squaring can introduce extraneous solutions. Always check the basic sign constraints beforehand (like noticing \(x \ge \text{positive radical}\) forces \(x \ge 0\)) to instantly rule out misleading options like choice (1).

Answer 1

The Correct Option is D