Mathematics

Problem

Let

f:\mathbb R\to\mathbb R

be defined by

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

. a. (i) Show that

f

is not injective on

\mathbb R

. b. (ii) Find the range of

f

when the domain is

\mathbb R

. c. (iii) Specify a suitable interval

D

contained in

\mathbb R

such that

f

restricted to

D

is bijective onto its range. Give a clear justification for your choice of

D

. d. (iv) For the domain interval

D

chosen in part (iii), obtain the inverse function

f^{-1}:\operatorname{Range}(f)\to D