1.3 Creating New Polynomial Functions: An Introduction to ...

(b) What does the function D(C(p)) represent if a pair of shoes has a regular
price of $80 Determine D(C(80)).
(c) What does the function C D represent for a pair of shoes with a regular
price of $80 Determine C D for the same pair of shoes.
(d) Does C D D C Justify your answer.
Solution
(a) C(p) p 15 and D(p) 0.8p
(b) D(C(p)) means the coupon is applied first and then the
discount is applied to the cost of the shoes. So, when p 80,
D(C(80)) D(80 15)
D(65)
0.8(65)
52
(c) C D means the discount is taken first and then the coupon reduction is
applied. When p 80,
(C D)(x) C(D(80))
C(0.8(80))
C(64)
64 15
49
(d) In this case, C D ≠ D C. The order of composition makes a difference.
When p 80, D(C(80)) 52 and C(D(80)) 49. In fact, these two
functions are different.
(C D)(p) C(0.8p) (D C)(p) D(p 15)
0.8p 15 0.8(p 15)
0.8p 12
CHECK, CONSOLIDATE, COMMUNICATE
1. Explain how a new polynomial function can be made from two
polynomial functions by addition, by subtraction, and by multiplication.
2. State ( f g)(x), ( f g)(x), ( f g)(x), and f (g(x)) for
f {(1, 4), (0, 5), (6, 3)} and g {(1, 6), (0, 9), (4, 2)}.
3. Determine ( f g)(x), ( f g)(x), ( f g)(x), and f (g(x)) for
f (x) x 2 3x 2 and g(x) x 3.
1.3 CREATING NEW POLYNOMIAL FUNCTIONS: AN INTRODUCTION TO COMPOSITION 33