Let be defined by

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let

g:\mathbb R\to\mathbb R

be defined by

g(x)=x^{2}-4x+1

. Answer the following. (i) Is

g

one–to–one on

\mathbb R

? Give a brief reason referring to the shape of its graph. (ii) Describe, with justification, how an appropriate restriction of the domain can render

g

invertible. (iii) State any one interval that achieves this and write the corresponding co–domain so that the restricted

g

becomes a bijection.