A car dealership advertises a 30% discount on all its now cars. In addition, the

Question

A car dealership advertises a 30% discount on all its now cars. In addition, the manufacturer offers a $200 rebate on the purchase of a new car. Let X represent the sticker price of the car (a) Suppose that only the 30% discount applies. Find a function f that models the purchase price of the car as a function of the sticker price x. f(x) = (b) Suppose that only the $200 rebate applies. Find a function g that models the purchase price of the car as function of the sticker price X. g(x) = (c) Find a formula for H = f middot g H(x) = (d) Find H^-1 H^-1 (x) =

Explanation / Answer

a)f(x)=((100-30)/100)x

f(x)=0.7x

b)g(x)=x -200

c)H=fog

H(x)=f(g(x))

H(x)=0.7(x-200)

d)let H(x)=y

=>x=H-1(y)

0.7(x-200)=y

=>x-200 =y/0.7

=>x-200=10y/7

=>x=200+(10y/7)

H-1(y) =200+(10y/7)

H-1(x) =200+(10x/7)

H-1(x) =200+ 1.429x

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