Mathematics

Problem

Let

f:\mathbb R\to\mathbb R

be given by

f(x)=|ax+b|

, where

a\ne 0

and

b

are real constants. a. (i) Explain why the range of

f

[0,\infty)

. b. (ii) State the condition on

a

and

b

under which

f(x)=0

has a solution, and find that solution. c. (iii) If the domain of

f

is restricted to

x\ge -\dfrac{b}{a}

, determine the new range of

f

and justify your result.