Determine the domain of the function:
Let’s find the domain of the function:
Because there is a denominator, the denominator must be different from zero:
Also, there is a square root, so we need the expression inside the root to be non-negative:
This inequality is equivalent to the inequality:
Therefore, we solve the latter:
Because we are looking for the section above the x-axis or on it and the parabola “cries”, we get that the solution of the inequality is
-1\leq x\leq 1
Finally, let us not forget that we also demanded that
So together the answer is
-1\leq x< 1
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