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What is the domain?

Find the domain of the function \(f(x) = \sqrt{2 - 2x - x^2} \).

Note by Pritthijit Nath
4 months, 1 week ago

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For \(f(x)\) to be defined,

\[2-2x-x^2≥0 \Rightarrow x^2+2x-2≤0 \\ (x+1)^2-(\sqrt{3})^2≤0 \\ (x+1+\sqrt{3})(x+1-\sqrt{3})≤0 \\ \therefore x \in \left[-1-\sqrt{3},-1+\sqrt{3}\right] \] Akshat Sharda · 4 months, 1 week ago

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@Akshat Sharda Completing squares method is the best. Akshay Yadav · 4 months, 1 week ago

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