Let be defined by .

MATHEMATICS · Multi-part · AoPS · Mathematics · Special Functions · Special Functions

Problem

Let

h:\mathbb{R}\to\mathbb{R}

be defined by

h(x)=\lfloor 3x\rfloor-\operatorname{sgn}(x)

. (i) Compute

h(-1.2)

h(0)

and

h(\dfrac{2}{3})

. (ii) Solve

h(x)=4

for

x

in the interval

[0,2]

. (iii) Determine the range of

h(x)

for

x\in[-1,1]

. Justify your answer.