If $f(x)=\left\{\begin{matrix}[\cos πx],&x<1\\|x-2|,&1≤x<2\end{matrix}\right.$ ([*] denotes the greatest integer function), then f(x) is
Answer & explanation
Correct answer: option 3
We have, $f(x)=\left\{\begin{matrix}[\cos πx],&x<1\\|x-2|,&1≤x<2\end{matrix}\right.$
$= 2 – x, 1≤x<2\left\{\begin{matrix}-1,&\frac{1}{2}<x<1\\0,&0<x≤\frac{1}{2}\\0,&-\frac{1}{2}≤x<0\\-1,&-\frac{3}{2}<x<-\frac{1}{2}\end{matrix}\right.$
It is evident from the definition that f(x) is discontinuous at x = 1/2.