Mathematics

Problem

Consider the functions

f(x)=2x^{2}-3x+1

and

g(x)=x|x|

defined on the set of all real numbers. a. (i) Find

(f+g)(x)

and

(f-g)(x)

, writing each answer in its simplest algebraic form. b. (ii) Evaluate

(f+g)(-2)

and

(f-g)(2)

. c. (iii) State the domain of

(f-g)(x)

, giving reasons for your answer.