The regular price of a computer is x dollars. Let f(x) = x - 400 and g(x) = 0.75x. Solve, a. Describe what the functions f and g model in terms of the

Step 1 Let $f(x)=x-400andg(x)=0.75x$
a) $f(x)=x-400$
Thus, f models the price of a computer after a discount of 400 dollars.
Also, $g(x)=0.75x$
The function g gives a value that is 075 into x that is 75% of x.
This means that g gives only 75% of the regular price.
Therefore, g models the price of a computer after a 25 % discount.
b) To find composite function ${\displaystyle (f\circ g)\left(x\right),}$
${\displaystyle (f\circ g)\left(x\right)=f\left(g\left(x\right)\right)=f\left(0.75x\right)}$
By using $f(x)=x-400$,
$f(g(x))=0.75x-400$.
thus, the composite function ${\displaystyle (f\circ g)\left(x\right)=0.75x-400.}$
The composite function f(g(x)) models that the price of a computer has 25% discount and then 400 dollars discount.
c) To find composite function ${\displaystyle (g\circ f)\left(x\right),}$
${\displaystyle (g\circ f)\left(x\right)=g\left(f\left(x\right)\right)=g(x-400)}$
By using $g(x)=0.75x$ ,
$g(f(x))=0.75(x-400)$.
thus, the composite function ${\displaystyle (g\circ f)\left(x\right)=0.75(x-400)}$
The composite function g(f(x)) models that the price of a computer has 400 dollars discount and then 25% discount.
d) Now find ${\displaystyle (f\circ g)\left(x\right)-(g\circ f)\left(x\right),}$
$(0.75x-400)-(0.75(x-400))$
$=0.75x-400-(0.75x-300)$
$=0.75x-400+0.75x+300$
$=-100$
Thus, ${\displaystyle (f\circ g)\left(x\right)-(g\circ f)\left(x\right)<0}$
Hence ${\displaystyle (f\circ g)\left(x\right)<(g\circ f)\left(x\right)}$
Hence the price of computer using function ${\displaystyle (f\circ g)\left(x\right)}$ is minimum.
Thus the composite function ${\displaystyle (f\circ g)\left(x\right)}$ gives more discount than ${\displaystyle (g\circ f)\left(x\right)}$ .