Determine the domain of the function:
Let’s find the domain of the function:
There is a square root, so we need the expression inside the root to be non-negative:
Also, the coefficient of the square expression is negative (-1), so the graph looks like an inverted parabola (= inverted bowl = “crying”).
It looks like this:
Back to inequality:
We need to check when the equation we solved is not negative, i.e. when the graph is not below the x-axis. And one can see from the graph that this happens when the following holds
-1\leq x\leq 1
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