Mathematics

Problem

Define

f:\mathbb R\to\mathbb R

f(x)=x^{3}+x

. a. (i) Prove that

f

is injective. b. (ii) Prove that

f

is surjective. c. (iii) Hence, establish that

f

is invertible and write an implicit equation satisfied by

f^{-1}(y)

for a given

y\in\mathbb R