Question

# The following definition is discussed in advanced mathematics courses.

Normal distributions

The following definition is discussed in advanced mathematics courses.

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

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: $$f(\pi )=1$$