One-to-One functions and their Inverses

[isaac_92502]

I have this problem "A car dealership advertises a 15% discount on all its new cars. In addition, the manufacturer offers a $1,000 rebate on the purchase of a new car. Let x represent the sticker price of the car."

a)Suppose only the 15% discount applies. Find a function f that models the purchase price of the car as a function of the sticker price x.
f(x)=(100%-15%)=.85x

b) Suppose the $1000 rebate applies. Find a function g that models the purchase price of the car as a function of the sticker price x.
g(x)=x-1000

c) Find a formula for H=f(g(x))

I'm stuck on finding the formula for f(g(x))

 

[tkhunny]

What is f(100)?
What is f(250)?
What is f(Peanut Butter Sandwich)?

 

[Dr.Peterson]

Do you know what composition of functions means?

f(g(x)) means that you replace x in the definition of f with the expression for g(x). So in the formula f(x) = 0.85x, replace x with x - 1000 and see what you get.

If you're not sure of your answer, try checking it against specific numbers. For example, if the sticker price is x=$50,000, then g(x) = 50,000 - 1000 = 49,000, and f(g(50,000)) = f(49,000) = 0.85*49,000 = 41,650. Your formula should give that result.

 

[HallsofIvy]

I have this problem "A car dealership advertises a 15% discount on all its new cars. In addition, the manufacturer offers a $1,000 rebate on the purchase of a new car. Let x represent the sticker price of the car."

a)Suppose only the 15% discount applies. Find a function f that models the purchase price of the car as a function of the sticker price x.
f(x)=(100%-15%)=.85x

You have a typo here- it should be
f(x)= (100%- 15%)x= .85x

b) Suppose the $1000 rebate applies. Find a function g that models the purchase price of the car as a function of the sticker price x.
g(x)=x-1000

c) Find a formula for H=f(g(x))

I'm stuck on finding the formula for f(g(x))

"f(g(x))" means "first apply g to x then apply f to that number. g(x)=x- 1000 and f just multiplies that by .85: f(g(x))= .85(x- 1000). If you want to (I would not consider it necessary) you can "distribute" the .85 to write f(g(x))= .85x- 850.

Does the problem really ask for "f(g(x))"? Given that ""A car dealership advertises a 15% discount on all its new cars. In addition, the manufacturer offers a $1,000 rebate on the purchase of a new car. Let x represent the sticker price of the car." I would interpret that as taking the 15% discount first, then giving the $1,000 rebate. That would be g(f(x))= .85x- 1000.

What does this have to do with "one to one functions and their inverses"?