Mathematics

Problem

Consider the quadratic function

f(x)=x^{2}-4x+5

restricted to the domain

x\ge 2

. Work through all parts. a. (i) Show that

f

is one–to–one on the given domain. b. (ii) Obtain the algebraic form of

f^{-1}(x)

and state its domain and range. c. (iii) Sketch the graphs of

f

and

f^{-1}

on the same pair of axes, marking at least three pairs of corresponding points. d. (iv) Determine all real numbers

k

for which the horizontal line

y=k

intersects both graphs at exactly one common point.