Consider the quadratic function given by

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Consider the quadratic function

g:\mathbb R\to\mathbb R

given by

g(x)=x^{2}-4x+7

. (i) Determine whether

g

is one–one on

\mathbb R

. Justify your answer. (ii) Find the vertex of the parabola

y=g(x)

and hence obtain an interval

I

on which

g

is one–one. (iii) Restricting the domain of

g

to the interval

I

, find

g^{-1}(x)

and state both the domain and range of the inverse.