Mathematics

Problem

Let

p:\mathbb R\to\mathbb R

be defined by

p(x)=x^{3}-3x

. Answer the following questions. a. (i) Show that

p

is an odd function. b. (ii) Prove that

p

is surjective. c. (iii) Find one real number

x

such that

p(x)=0

and one real number

x

such that

p(x)=4

. State your reasoning clearly.