Mathematics

Problem

Let

f(x)=4x^{3}-2x^{2}+1

and

g(x)=x^{3}+3x

. Define

h(x)=f(x)-2g(x)

. a. (i) Obtain a simplified expression for

h(x)

. b. (ii) Determine the degree and leading coefficient of

h(x)

. c. (iii) Decide whether

h(x)

is an even function, an odd function, or neither. Give a reason for your answer.