Finding discontinuities of a piecewise function on rationals and irrationals

[Charles49]

Homework Statement

Let f be the function defined on the real line by

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

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

Homework Equations

None

The Attempt at a Solution

How do you answer this?

 

[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?

 

[Charles49]

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

 

[micromass]

Yep, that's it!