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# Domain and Range

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What is the domain of the real-valued function $f(x)=\frac{2x-7}{\sqrt{x^2-5x+6}}$?

Feb 21, 2021

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$$x^2-5x+6\ge 0$$

$$(x-2)(x-3)\ge 0 \iff x\le 2,\ x\ge 3$$

or $$\boxed{x \in (-\infty, 2] \cup [3, \infty)}$$

Feb 21, 2021