# What is the domain?

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

Note by Pritthijit Nath
2 years, 1 month ago

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

$2-2x-x^2≥0 \Rightarrow x^2+2x-2≤0 \\ (x+1)^2-(\sqrt{3})^2≤0 \\ (x+1+\sqrt{3})(x+1-\sqrt{3})≤0 \\ \therefore x \in \left[-1-\sqrt{3},-1+\sqrt{3}\right]$

- 2 years, 1 month ago

Completing squares method is the best.

- 2 years, 1 month ago