Discussion
The function \(f(x) = x(\sqrt{x + 2} + \sqrt{x + 1})\) is continuous on
Answer: D
The function is continuous on \([-1, \infty)\).
\(\sqrt{x + 2}\) needs \(x \ge -2\) and \(\sqrt{x + 1}\) needs \(x \ge -1\); both must be defined, so the domain is \(x \ge -1\). On that interval f is a product and sum of continuous functions, so it is continuous there.
\([-3, \infty)\) and \((-\infty, \infty)\) include points where a square root is of a negative number, and \((-\infty, 1]\) does too. \([4, \infty)\) lies inside the domain, so f is continuous there too, but it is only part of the interval of continuity; the question asks for the whole of it, which is \([-1, \infty)\).
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