MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
Define f:R→R by f(x)=x3+x.
(i) Prove that f is injective.
(ii) Prove that f is surjective.
(iii) Hence, establish that f is invertible and write an implicit equation satisfied by f−1(y) for a given y∈R.