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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.

Sep 17, 2021

#1
+13724
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Find the domain of the real-valued function

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

Hello Guest!

$$f(x) = -\sqrt{ -10x^2 - 4x + 6 }\\ -10x^2 - 4x + 6=0$$

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}\\ x = {4 \pm \sqrt{16-4\cdot (-10)\cdot 6} \over 2\cdot (-10)}\\ x\in \{-1,\frac{3}{5}\}$$

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

!

Sep 17, 2021
edited by asinus  Sep 17, 2021