Consider the function defined by .

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Consider the function

f: \mathbb{R}\to\mathbb{R}

defined by

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

. (i) Define an injective function and a surjective function. (ii) Examine

f

on its given domain and codomain. Determine, with justification, whether

f

is injective and whether it is surjective. (iii) State which of the two properties fails (or both fail) for

f

and explain why this prevents

f

from being invertible on

\mathbb{R}