Let be defined by .

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

Problem

Let

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

be defined by

f(x)=2x^{2}-8x+5

. (a) Rewrite

f(x)

in the completed–square form and hence find the coordinates of its vertex. (b) Determine the least interval containing

x=3

on which

f

becomes one–one. (c) For the interval obtained in part (b), find the explicit expression for

f^{-1}

and state its domain and range.