6. You have a coupon for your favorite clothing store for $20 off any purchase of more than $50. The store is also running a 25%-off sale on its entire inventory. Let x be the original price, f(x) be the price with the $20 coupon applied, and g(x) be the price with the 25% discount applied.
Find the expression for f(x) and g(x)
f(x) = x - 20; x = 50
g(x) = (0.75)(x)

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

Question

6.	You have a coupon for your favorite clothing store for $20 off any purchase of more than $50. The store is also running a 25%-off sale on its entire inventory. Let x be the original price, f(x) be the price with the $20 coupon applied, and g(x) be the price with the 25% discount applied.
Find the expression for f(x) and g(x)
f(x) = x - 20; x >= 50 
g(x) = (0.75)(x)

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

luigi0210 · Answer

Sorry Sham, I gtg do something. But I'd say you might wanna re-check it

shamil98 · Answer

Okay.

rsadhvika · Answer

g(x) = x(0.75)
f(x) = x-20

rsadhvika · Answer

keep them simple,
you teacher wants to explain you the concept of composition after this

rsadhvika · Answer

Now, if u want to know whats the cost, after applying both discount+coupon
we could simply do f(g(x))

rsadhvika · Answer

g(x) > 50 is the constrain btw

rsadhvika · Answer

f(x) is the price wid discount applied,
that makes f(x) = x-20  if x > 50, other wise f(x) = x

shamil98 · Answer

.75 of f(x) = g(x) 
because it says its 25% off.

rsadhvika · Answer

similarly g(x) is the price wid discount applied,
that makes g(x) = 0.75

rsadhvika · Answer

dont mess wid f(x), when constructing g(x)

rsadhvika · Answer

do them independently

rsadhvika · Answer

*
similarly g(x) is the price wid discount applied, 
that makes g(x) = 0.75x

shamil98 · Answer

Oh, okay, i get it.

rsadhvika · Answer

good :)
overall,

$f(x) = x  ; x <= 50$
$f(x) = x-20 ;  x > 50$

$g(x) = .75x$

rsadhvika · Answer

do they look okays ?

shamil98 · Answer

Could you help with the other parts of the question? I've edited it. Yes it makes more sense because x is the original price .

rsadhvika · Answer

(f o g)(x) = f(g(x))

rsadhvika · Answer

look carefully, first we're applying g, then giving it to f

rsadhvika · Answer

so, first we're doing .75x, then we're doing x-20
that means, first we're doing 25% discount, and on top of that, if that amount is > 50, we're subtracting 20

shamil98 · Answer

It wouldn't be .75x - 20; .75x >= 50?..

rsadhvika · Answer

in simple terms, (f o g)(x) , represents first applying 25% discount, and on top of that, applying the gift coupon

rsadhvika · Answer

forget about expression, they dont want it here

shamil98 · Answer

Oh, yeah... mb.

rsadhvika · Answer

:) can u try next part urself,

shamil98 · Answer

Yeah. for (g o f) (x) represents first applying 20 dollar coupon then the 25% discount?

rsadhvika · Answer

perfect !

cuz (g o f)(x) = g(f(x))

we observe that, first we're giving x to f, after that, we're giving it to g.

shamil98 · Answer

Thank you :)

rsadhvika · Answer

btw, can we knw which one saves us money ? :)

(g o f)(x)  or  (f o g)(x)

shamil98 · Answer

I think  ( f o g) (x) saves more money because it's based off of percentage.

rsadhvika · Answer

Yup !!! nice work :)

rsadhvika · Answer

but careful ! you may miss 20 deduction, if that percentage discount makes the amount < 50

shamil98 · Answer

Yeah, that's true. So it would have to be a higher number that when it's reduced by 25% its greater than or equal to 50.

rsadhvika · Answer

exactly ! you get the point :)