Question

The following definition is discussed in advanced mathematics courses.

Normal distributions
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asked 2021-05-01

The following definition is discussed in advanced mathematics courses.

\(f(x)=\begin{cases}0 & if\ x\ is\ a\ rational\ number\\1 & if\ x\ is\ an\ irrational\ number \end{cases}\)
Evaluate  \(f(-\frac{3}{4}), f(-\sqrt{2}),\ and\ f(\pi) \).

Answers (1)

2021-05-02

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

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