Let be defined by .

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

Problem

Let

h:\mathbb{R}\to\mathbb{R}

be defined by

h(x)=x^{2}-4x+3

. (i) Explain why

h

is not invertible when its domain is the entire set of real numbers. (ii) Determine an interval

I

contained in

\mathbb{R}

such that the restriction

h|_{I}

is one–one. Justify your choice. (iii) With the domain restricted to

I

, find the inverse function

h^{-1}(x)

and specify its domain and range.