Answer
a) 1; b) -4; c) 3; d) 2
Work Step by Step
We are given the function:
$k(x)=[[2x+1]]$ denotes the greatest integer less than or equal to $2x+1$.
a) $k\left(\dfrac{1}{3}\right)=\left[\left[2\left(\dfrac{1}{3}\right)+1\right]\right]=\left[\left[\dfrac{5}{3}\right]\right]=1$
b) $k\left(-2.1\right)=[[2(-2.1)+1]]=[[-3.2]]=-4$
c) $k(1.1)=[[2(1.1)+1]]=[[3.2]]=3$
d) $k\left(\dfrac{2}{3}\right)=\left[\left[2\left(\dfrac{2}{3}\right)+1\right]\right]=\left[\left[\dfrac{7}{3}\right]\right]=2$
