Let be defined by .

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

Problem

Let

f:[1,\infty)\to[0,\infty)

be defined by

f(x)=x^{2}-1

. (i) Prove that

f

is injective on its domain. (ii) Prove that

f

is surjective onto its codomain

[0,\infty)

. (iii) Find the inverse function

f^{-1}

and state the appropriate domain and codomain for

f^{-1}