# Homework Help: Rational and Irrational numbers

1. Sep 10, 2011

### Charles49

1. The problem statement, all variables and given/known data
Let f be the function defined on the real line by

$$f(x)= \begin{cases} \frac{x}{3} & \text{if x is rational } \\ \frac{x}{4} &\text{if x is irrational.} \end{cases}$$

Let D be the set of points of discontinuities of f. What is D?

2. Relevant equations

None

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 10, 2011

### micromass

Well, perhaps it would be good if you would first try to "plot" the function. You can't plot it accurately, but you can get an idea. What does the plot look like? What can you conclude?

3. Sep 10, 2011

### Charles49

Ok I got it, D is the entire real number set excluding 0.

4. Sep 11, 2011

### micromass

Yep, that's it!!