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Compute the domain of the function $$f(x)=\frac{1}{\lfloor x^2-17x+18\rfloor}.$$

 Apr 19, 2022
 #1
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f(x) = [x^2 - 17x + 18] ^-1

f'(x) = [2x - 17]^-1

f'(x) = 1/(2x - 17) 

 Apr 19, 2022
 #2
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For the domain, \(\text{denominator} \neq 0\). Then we have \(\lfloor x^2 - 17x + 18\rfloor \neq 0\).

 

By properties of floor function, we have \(x^2 - 17x + 18 < 0\text{ or }x^2 - 17x + 18 \geq 1\).

Now you can solve the compound inequality to get the domain of f(x).

 Apr 19, 2022

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