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# Domain

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What is the domain of the function f(x) = (x + 6)/sqrt(x^2 - 4)?

May 12, 2022

#1
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What is the domain?

Hello Guest!

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

$$\color{blue}\mathbb D=\mathbb R\ |\ x\in \{-2\leq x\leq 2\}$$

!

May 12, 2022
#3
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Note that when x = -2 or x = 2, the denominator will become 0.

MaxWong  May 12, 2022
#2
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Things inside any square root must be nonnegative and the denominator is nonzero.

$$x^2 - 4 \geq 0\text{ and } \sqrt{x^2 - 4} \neq 0 \\ x^2 - 4 \geq 0 \text{ and }x^2 - 4 \neq 0\\ x^2 - 4 > 0$$

Continue to solve the inequality, and you will get the domain of the function.

$$\operatorname{Domain}(f) = \{x \in \mathbb R:-2 < x < 2\}$$

May 12, 2022
#5
+13730
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$$\operatorname{Domain}(f) = \{x \in \mathbb R:-2 < x < 2\}\\ correctly\\ Domain\ f(x) = \mathbb R\ |\ -2 \leq x \leq 2$$

!

asinus  May 12, 2022
edited by asinus  May 12, 2022