The following definition is discussed in advanced mathematics courses.

Anish Buchanan 2021-10-05 Answered

The following definition is discussed in advanced mathematics courses. \(f(x)=\begin{cases} 0 & \text{if xx is a rational number}\ 1 & \text{if xx is an irrational number} \end{cases}\)
Evaluate \(f(−34)\), \(-\sqrt2\), and \(\displaystyle{f{{\left(\pi\right)}}}\).

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Expert Answer

ensojadasH
Answered 2021-10-06 Author has 6446 answers

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 \(x=-\sqrt 2\) is an irrational number, then: \(f(-\sqrt 2)=1\)
Since \(x=\pi\) is an irrational number, then: \(f(\pi )=1\)

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The following definition is discussed in advanced mathematics courses.

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