Question

The question - http://i.imgur.com/9fdNT9Z.png
Write a expression for f(x)
write an expression for g(x)
what would the expression(fog)(x) represent?
what would the expression (gof)(x)
If the store allows you to apply both the 20% discount and the $25-off coupon, does it matter which you apply first? How do you know?

Sorry for all the questions it's my last one thank you guys!

Answer 1

a)
f(x) = x - 25; x > 50
(also, f(x) = x; x <-50)

b)
g(x) = 0.2x

c)
(f o g) represents taking the 25$ discount after the 20% off has been applied

d)
(g o f) represents taking the 25$ discount before the 20% has been applied.

e)
Assume (f o g) = (g o f)
(also assume the purchase is for more than 50$)
f(g(x)) = g(f(x))
f(0.2x) = g(x - 25)
(0.2x) - 25 = 0.2(x - 25)
0.2x - 25 = 0.2x - 12.5
-25 = - 12.5
This is a contradiction, so the original assumption must not be true: therefore, it does matter which function you apply first.