Question

You have a coupon for your favorite clothing store for $35 off any purchase of $70 or more. The store is running a 25% off sale on its entire inventory. Let x be the original price, f(x) be the price with the coupon applied, and g(x) be the price with the discount applied.

a.) Write an expression for f(x).

b.) Write an expression for g(x).

c.) What would the expression (f o g)(x) represent?

d.) What would the expression (g o f)(x) represent?

e.) If the store allows you to apply both the discount and the coupon, does it matter which you apply first? How do you know?

Answer 1

okay so do you know what youre expression f(x) should look like?

Answer 2

No. :c I don't think so... This problem has me totally stumped, I actually thought I didn't have enough information...

Answer 3

f(x)=35+70 Maybe? ...
o. o;

Answer 4

70-30?

Answer 5

35*

Answer 6

Ok. >.< lol, I'm gonna take it just a little slower...
Would my price be 70? the 35 would be the price taken off, and the only other price I have is the "$70 or more"

Answer 7

no forget about the 70 for a sec. YOU HAVE A RANDOM PRICE OK, its x.
and you are taking 35 away from it. what does that look like

Answer 8

x - 35 c:

Answer 9

PERFECT :) so f(x)=x-35. now the price, (x), needs to be more than or equal to 70. so on the side of the equation, what would you put?

Answer 10

\[f(x) = x - 35 \ge 70\]

Answer 11

Oh... ;O I... Kind of see why that would work...
Why would there be another x be put in front of the 70?

Answer 12

actually think it will look like
\[f(x \ge70)=x-35\]

Answer 13

And that's what A would be, right?

Answer 14

yesss.. now b. you have to take 25% off a price(x).
so what would that look like?

Answer 15

Would I carry over the equation that we got in A?

Answer 16

mp because this is a totally different equation!
b. Write an expression for g(x)
so g(x)= (25% dis, off a price(x))

Answer 17

So... 25 - x?
Or x - 25?

Answer 18

do you know how to take percentages off a price? cause 25% does not = $25

Answer 19

Lol, I'd turn it into a decimal and multiply it by something right?

Answer 20

In this case, x?

Answer 21

So then... g(x)=x-.25? Or keep it 25%?

Answer 22

SOOOOOO close. remember: "of" always means multiply

and you are taking 25% OF x

Answer 23

g(x)=x(.25) ? >o<

Answer 24

yep! perfect.
b. \[g(x)=.25x\]

Answer 25

^ u ^ Awesome!

Answer 26

so c meow? ^-^

Answer 27

Yush! >^<

Answer 28

c.) What would the expression (f o g)(x) represent?

For (fog)(x), take g and SHOVE IT INTO f..
so like
f(g(x))=?

Answer 29

now youre combining a and b.. BUT ONLY HAVE ONE x

Answer 30

Lol xD
f(g(.25x)?

Answer 31

))*

Answer 32

So then it would be f(g(.25x-35))?

Answer 33

dont put the equation in f(g(x)). leave that alone. have that = the equation

Answer 34

f(g(x))=.25x-35...

Answer 35

EXACTLY! now dont forget that it still all has to be greater than or equal to 70. so ur equation should end up looking like:

\[f(g(x)\ge70)=.25x-35\]

Answer 36

And that's my expression...

Answer 37

thats what c should be.. yes

Answer 38

Awesome! n.n I feel smart.. Thank yhu for helping me by the way...
Shall we work on D? :3

Answer 39

yepp :) and no problem this is fun kind of math so i love it.

now for D,
g(f(x))=( a price(x), taking away 35, and then 25% OF that.)

Answer 40

g(f(x))=x-35(.25x)

Answer 41

SUPER close.. but you only need 1 x in the equation, cause there is only one random total? okay? so it should look like this,

\[g(f(x))=.25(x-35)\]

you got that exact answer except you had an extra x

Answer 42

Oh, I see what yhu did... ^~^

Answer 43

awesome :)
now dont forget that it still all has to be greater than or equal to 70!!

do you know what the problem would look like then? its just like we did to the last :)

Answer 44

\[f(g(x)\ge70)) = .25x - 35\]

Answer 45

uh oh! SO CLOSE! you switched up (g o f)(x) with (f o g)(x)

Answer 46

>n<;;
\[g(f(x)\ge70) = .25x - 35\]

Answer 47

YEP! so you should end up with d being:

\[g(f(x)\ge70)=.25(x-35)\]

Answer 48

Would yhu do the same thing for c?
put parenthesis around the x-35 with .25 outside of them?

Answer 49

Uhm..... This is what I have for C...
\[f(g(x)\ge70) = .25x - 35\]

Answer 50

i just changed it.. can you see how c and d are similar? they are a and b's equation put together, according to g o f(x) or f o g(x)

Answer 51

>o< Oh gosh...

Answer 52

; n ; I see a lot of question marks...

Answer 53

oh my glob hold on...

Answer 54

xD 'kay

Answer 55

; ~ ; No... It did it again... >.<
Where the question marks are, should there be a subtraction sign?

Answer 56

WAIT! I see it now! ^.^

Answer 57

okay awesome:) but really cant you tell how theyre similar? :)

Answer 58

Lol yes. n.n Now I can. c:

Answer 59

can you do e on your own?

Answer 60

Uhm... It wouldn't matter would it?

Answer 61

SCRATCH WHAT I SAID ABOUT CHANING C I WAS RIGHT BEFORE.

and actually

It matters, here you apply the discount first , then you apply the $35-off coupon. In order to apply the $35-off coupon, after you apply the 25% off, you purchase have to be greater than or equal to 70.

Answer 62

Oh! ... Oh I get it....

Answer 63

So altogether, this is what your answer should look like.

a.) Write an expression for f(x).

\[f(x \ge70)=x-35\]

b.) Write an expression for g(x).

\[g(x)=.25x\]

c.) What would the expression (f o g)(x) represent?

\[f(g(x)\ge70)=(.25x)-35\]

d.) What would the expression (g o f)(x) represent?

\[g(f(x \ge70))=.25(x-35)\]

e.) If the store allows you to apply both the discount and the coupon, does it matter which you apply first? How do you know?

It matters, here you apply the discount first, then you apply the $35-off coupon. In order to apply the $35-off coupon, after you apply the 25% off, your purchase has to be greater than or equal to $70.

AND YOURE DONE!!!! :)

Answer 64

~^O^~
Oh my gush, Thank yhu so much for yhur help. Yhur so awesome. X3 I appreciate it so much. And thank yhu for walking me through it and not just handing me the answers...

Answer 65

no problem babe.. id love to help you again sometime! ^_^
you did great! come back to this for reference if you ever have anymore problems like this okay? bye!

Answer 66

Will do! n_n
Bye! Cx

Answer 67

I would love to fan yhu, but openstudy is being a lametart... So I'll fan yhu when it allows me to. c:

Answer 68

awe! thank you<3

Answer 69

No problem! <3