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# Domain

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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