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If f(x) = 2 - x^(1/2) and g(x) = x^2 - 9, what is the domain of g(x)/f(x)?

 May 12, 2022
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So \(f(x) \neq 0\) and \(x \geq 0\) since \(x^{1/2} = \sqrt x\).

 

\(f(x) \neq 0\\ 2 - x^{1/2} \neq 0\\ x \neq 4\)

 

Combine \(x \geq 0\) and \(x \neq 4\) to get \(x \in [0, 4) \cup (4, +\infty)\).

 

Therefore, the domain of g(x)/f(x) is \([0, 4) \cup (4, +\infty)\), or written in inequality form, \(\{x \in \mathbb R : 0 \leq x < 4 \text{ or }x > 4\}\).

 May 12, 2022

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