AoPS

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

Problem

Define

q(x)=\left\lfloor \dfrac{|3x-4|}{2} \right\rfloor \times \operatorname{sgn}(1-x)

. (i) Find

q(-1)

. (ii) Find

q(1)

. (iii) Find

q\!\left(\dfrac{4}{3}\right)

. (iv) Hence obtain the product

q(-1)\,q(1)\,q\!\left(\dfrac{4}{3}\right)

.}],