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

ka1leE 2020-11-08 Answered

The regular price of a computer is x dollars. Let f(x)=x400 and g(x)=0.75x. Solve,
a. Describe what the functions f and g model in terms of the price of the computer.
b. Find (fg)(x) and describe what this models in terms of the price of the computer.
c. Repeat part (b) for (gf)(x).
d. Which composite function models the greater discount on the computer, fg or gf?

You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Jaylen Fountain
Answered 2020-11-09 Author has 170 answers

Step 1 Let f(x)=x400 and g(x)=0.75x
a) f(x)=x400
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 (fg)(x),
(fg)(x)=f(g(x))=f(0.75x)
By using f(x)=x400,
f(g(x))=0.75x400.
thus, the composite function (fg)(x)=0.75x400.
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 (gf)(x),
(gf)(x)=g(f(x))=g(x400)
By using g(x)=0.75x ,
g(f(x))=0.75(x400).
thus, the composite function (gf)(x)=0.75(x400)
The composite function g(f(x)) models that the price of a computer has 400 dollars discount and then 25% discount.
d) Now find (fg)(x)(gf)(x),
(0.75x400)(0.75(x400))
=0.75x400(0.75x300)
=0.75x400+0.75x+300
=100
Thus, (fg)(x)(gf)(x)<0
Hence (fg)(x)<(gf)(x)
Hence the price of computer using function (fg)(x) is minimum.
Thus the composite function (fg)(x) gives more discount than (gf)(x) .

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more