Composition of Functions

Question

An artist shops online for tubes of watercolor paint. The cost is $16 for each 14-mL tube.

a. Write a function representing the cost C(x) (in $) for x tubes of paint.
b. There is a 5.5% sales tax on the cost of merchandise and a fixed cost of $4.99 for shipping. Write a function representing the total cost T(a) for a dollars spent in merchandise.
c. Find (TºC)(x) and interpret the meaning in context.
d. Evaluate (TºC)(18) and interpret the meaning in context.

Answer 1

a) Each tube of paint cost $16.  If you buy x tubes then:

C(x) = 16x

 

b) If  we spend $a on merchandise, C(x) = a

We add to that 5.5% of a, and a fee of $4.99

T(a) = 1.055a + 4.99 

 

c)  (T^oC)(x) = T(16x) = 1.055(16x) + 4.99

     (T^oC)(x) = 16.88x + 4.99

 

This function for total cost means that there is $0.88 sales tax

on each tube of paint so the actual merchandise cost is $16.88

per tube.  To get total cost multiply the number of tubes ordered

by 16.88 and to that product add the fixed shipping fee of $4.99

 

d)  (T^oC)(18)

      This is simply asking to find the total cost, including sales tax

      and shipping, to order 18 tubes of paint.

     (T^oC)(18) = 16.88(18) + 4.99 = $308.83