Question

the regular price of a computer is x dollars. let f(x)=x - 240 and g(x)=0.75x.
a. describe what the functions f and g model in terms of the price of the computer.
the function f gives the price of the computer after a $240 discount.
the function g gives the price of the computer after a 25% discount.
b. find (f ∘ g)(x) and describe what this models in terms of the price of the computer.
(f ∘ g)(x)=0.75x - 240
the function (f ∘ g)(x) models the price of the computer after first a 25% discount and then a $240 discount.
c. find (g ∘ f)(x) and describe what this models in terms of the price of the computer.
(g ∘ f)(x)=□

Explanation:

Step1: Recall the definition of function composition

The composition $(g\circ f)(x)=g(f(x))$.

Step2: Substitute $f(x)$ into $g(x)$

Since $f(x)=x - 240$ and $g(x)=0.75x$, then $g(f(x))=0.75(x - 240)$.

Step3: Expand the expression

Using the distributive property $a(b - c)=ab - ac$, we have $0.75(x - 240)=0.75x-0.75\times240=0.75x - 180$.

Answer:

$0.75x - 180$