Which of the following correctly gives the piecewise definition of the function ?

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

Which of the following correctly gives the piecewise definition of the function

f(x)=|x-2|

? (a)

\begin{cases}x-2,& x<2\\ 2-x,& x\ge 2\end{cases}

(b)

\begin{cases}2-x,& x<2\\ x-2,& x>2\end{cases}

(c)

\begin{cases}2-x,& x\le 2\\ x-2,& x>2\end{cases}

(d)

\begin{cases}x-2,& x\le 2\\ 2-x,& x\ge 2\end{cases}