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# Domain

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Find the domain of the real-valued function

f(x) = -sqrt(-10x^2 - 4x + 6)

Give the endpoints in your answer as common fractions, not mixed numbers or decimals.

May 16, 2022

#1
+13731
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Find the domain of the real-valued function

Hello Guest!

$$f(x) = -\sqrt{-10x^2 - 4x + 6}\\ (-10x^2 - 4x + 6)\geq 0\\ x^2+ \frac{2}{5}x-\frac{3}{5}\\ x=-\frac{1}{5}\pm \sqrt{\frac{1}{25}+\frac{3}{5}}\\ x=-\frac{1}{5}\pm \sqrt{\frac{16}{25}}$$

$$x\in\{-1,\frac{3}{5}\}$$

$$\color{blue}D=\{x\in \mathbb R\ |\ -1\leq x\leq \frac{3}{5}\}$$



!

May 16, 2022