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floor and ceiling problem

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Compute the domain of the function

$$f(x)=\frac{1}{\lfloor x^2-7x+13\rfloor}$$

Mar 17, 2020

#1
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The domain will consist of all real numbers except those that make the denominator equal to zero.

If you use the quadratice formula to find the solutions of the denominator, you find that the solutions are imaginary numbers.

This means that there are no real numbers that make the denominator zero, so you do not have to exclude any numbers from the domain.

The domain consists of all real numbers.

Mar 17, 2020
#2
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what if x^2-7x+13 was between 0 and 1, wouldn't that mean the floor of x^2-7x+13 is 0?

Mar 17, 2020