Question

Find the domain of √(2-2x-x^2 )

Answer 1

Let f(x)=2−2x−x2−−−−−−−−−√

If we want the range of f(x) to be real then, 0≤2−2x−x2

⟹x2+2x≤2

⟹x2+2x+1≤3

⟹(x+1)2≤3

⟹−3–√≤x+1≤3–√

⟹−3–√−1≤x≤3–√−1

So the domain of x is [−1−3–√,−1+3–√] .