Let the function be defined by .

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

Problem

Let the function

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

be defined by

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

. (i) Define a one–one function and an onto function. (ii) Show that

f

is neither one–one nor onto when considered on

\mathbb{R}

as domain and codomain. (iii) Determine the largest subset

A \subset \mathbb{R}

for which the restriction

f|_{A} : A \to f(A)

is invertible, and state the corresponding range.