Question

# The following definition is discussed in advanced mathematics courses.

Normal distributions

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: $$\displaystyle{f{{\left(\frac{}{\pi}\right)}}}={1}$$