Rational, or Irrational?

Algebra Level 1

Let \(\mathbb{R}^+\) be the set of all non-negative real numbers, and let \(f:\mathbb{R}^+ \to \mathbb{R}^+\) be defined as \[f(x)= \begin{cases} \frac{1}{q} & \text{ if } x= \frac{p}{q}, \\ \\ 0 & \text{ if } x=0 \text{ or } x \text{ is an irrational number}, \end{cases}\] where \(p\) and \(q\) are coprime positive integers. What is the value of \[f\left(\frac{12}{13}\right)+f(\pi)+f(0.25)?\]

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