Discussion
The domain of the function \(f(x) = \sqrt{x^{2} + x - 2}\) is
Answer: D
The domain is \((-\infty, -2] \cup [1, \infty)\).
The square root is real only when the expression under it is non-negative.
\[ x^{2} + x - 2 = (x + 2)(x - 1) \ge 0 \]
A product of two factors is non-negative when both have the same sign or one is zero, which happens for \(x \le -2\) or \(x \ge 1\). Both end points belong to the domain, since \(\sqrt{0} = 0\) is defined. The options with round brackets at -2 or 1 wrongly leave out those points, and \((-\infty, 1) \cup [0, \infty)\) is the whole real line.
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