alleryStart learning →What is the domain of the function $g(x) = x^3 + \sqrt{x + 2} - 10$?
AAll real $x$
BAll $x \neq -2$
CAll $x > 0$
DAll $x \geq -2$
Answer & Solution
Correct answer: D. All $x \geq -2$
The cube and the constant term are defined for every real $x$.
The square root $\sqrt{x + 2}$ requires its argument to be nonnegative: $x + 2 \geq 0$, that is $x \geq -2$.
So the domain consists of all real numbers at least $-2$.
At $x = -2$ the root equals 0, which is allowed.
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