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 $f\left(\frac{12}{13}\right)+f(\pi)+f(0.25)?$

\frac{19}{52}

\frac{13}{52}

\frac{17}{52}

\frac{15}{52}

2 solutions

John Aries Sarza
May 24, 2014

$\frac{1}{13} +0+\frac{1}{4}=\frac{17}{52}$

Varun Maru
Mar 14, 2014

f(x) for f(12/13)=1/13 as 12/13 is in p/q form f(x) for f(pi)=0 as pi is irrational f(x) for f(0.25)= 1/4 as .25=1/4 and is in p/q form so ans is 1/13+0+1/4=17/52

Rational, or Irrational?

2 solutions

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