Consider the function defined by .

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Consider the function

f : \mathbb R \to \mathbb R

defined by

f(x)=x^{3}+4

. (i) Prove that

f

is one–one and onto. (ii) Hence state the domain and the range of

f

. (iii) Without finding an explicit formula for

f^{-1}

, write the domain and the range of

f^{-1}

and give reasons for your answer.