Mathematics

Problem

Let

p: \mathbb R \to \mathbb Z

be defined by

p(x)=\Bigl\lfloor \log_{2}\bigl(x^{2}+1\bigr)\Bigr\rfloor

. a. (i) Express

p

as a composition of two named standard functions and state clearly which two they are. b. (ii) Determine all real numbers

x

for which

p(x)=0

. c. (iii) Determine all real numbers

x

for which

p(x)=1

p(x)=2

, and

p(x)=3

respectively. d. (iv) Sketch the graph of

p

for

0\le x\le 3

, carefully indicating the value taken on each interval. e. (v) State the complete domain and range of

p