Question

Ray is purchasing a laptop that is on sale for 25% off. He knows the function that represents the sale price of his laptop is c(p) = 0.75p, where p is the original price of the laptop. He also knows he has to pay 8% sale's tax on the laptop. The price of the laptop with tax is f(c) = 1.08c, where c is the sale price of the laptop.
Determine the composite function that can be used to calculate the final price of Ray's laptop by solving for f[c(p)].

f[c(p)] = 1.83p
f[c(p)] = 1.83cp
f[c(p)] = 0.81p
f[c(p)] = 0.81cp

Answer 1

Answer: $f[c(p)]=0.81p$

Step-by-step explanation:

Given: Ray is purchasing a laptop that is on sale for 25% off.

The function that represents the sale price of his laptop :

$c(p) = 0.75p$, where p is the original price of the laptop.

The price function of the laptop with tax :

$f(c) = 1.08c$, where c is the sale price of the laptop.

Now, consider the composite function that can be used to calculate the final price of Ray's laptop .

$\text{ i.e. }f[c(p)]=f[0.75p]\\\\\Rightarrow f[c(p)]=1.08(0.75p)\\\\\Rightarrow f[c(p)]=0.81p$

Answer 2

C(p) = 0.75p   where p is the original price of the laptop
f(c) = 1.08c    where c is the sales price of the laptop

the composite function is:

f(c(p)) = 1.08(0.75p)
f(c(p)) = 0.81p