Mathematics

Problem

Consider the function

f:\mathbb R\to\mathbb R

given by

f(x)=|x|+1

. a. (i) Determine the range of

f

. b. (ii) Decide whether

f

is surjective onto its co-domain

\mathbb R

. Give a reason. c. (iii) Decide whether

f

is injective on

\mathbb R

. Give a reason. d. (iv) Find the smallest interval

D\subseteq\mathbb R

for which

f

becomes invertible when its domain is restricted to

D

. Obtain the explicit expression for

f^{-1}

on this interval.