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The following definition is discussed in advanced mathematics courses.

Normal distributions
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asked 2021-06-28

The following definition is discussed in advanced mathematics courses. \($f(x)=\begin{cases}\ 0 & \text{if} \times \text{is a rational number}\\ 1 & \text{if} \times\text{ is an irrational number}\\ \end{cases}$\)
Evaluate \(f(−34), f(−2–\sqrt )\), and \(\displaystyle{f{{\left(\pi\right)}}}\).

Expert Answers (1)

2021-06-29

Since \(\displaystyle{x}=-{\frac{{{3}}}{{{4}}}}\) is a rational number (can be written as a ratio of two integers), then: \(\displaystyle{f}-{\frac{{{3}}}{{{4}}}}={0}\)
Since \(\displaystyle{x}=\frac{-}{\sqrt{{2}}}\) is an irrational number, then: \(\displaystyle{f{{\left(\frac{-}{\sqrt{{2}}}\right)}}}={1}\)
Since \(\displaystyle{x}\frac{=}{\pi}\) is an irrational number, then: \(\displaystyle{f{{\left(\frac{}{\pi}\right)}}}={1}\)

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