contestada

E) A department store has marked down its merchandise by 25%. It later decreases by $5
the price of items that have not sold.
a) Write a function f (x) to represent the price after the 25% markdown.
b) Write a function g(x) to represent the price after the $5 markdown.
c) Use a composition function to find the price of a $125 item after both price adjustments.
d) Does the order in which the adjustments are applied make a difference?
Explain.

Respuesta :

a. f(x) = 0.75xb. g(x) = x - 5c. $88.75d. Yes, if you do f(x) before g(x) or g(x) before f(x), you get different final prices.

MrRoyal

Composite function involves combining different functions to create a new one

Let the price of the items be x.

(a) Function f(x)

25% mark down implies that:

[tex]f(x) = (1 -25\%) \times x[/tex]

So, we have:

[tex]f(x) = (1 -0.25) \times x[/tex]

[tex]f(x) = 0.75 \times x[/tex]

[tex]f(x) = 0.75x[/tex]

Hence, the equation of function f(x) is f(x) = 0.75x

(b) Function g(x)

A $5 reduction in the price of the item implies that:

[tex]g(x) =x - 5[/tex]

Hence, the equation of function g(x) is g(x) = x - 5

(c) The final price of $125 item

This implies that x = 125

Substitute 125 for x in f(x)

[tex]f(x) = 0.75x[/tex]

[tex]f(125) = 0.75 \times 125[/tex]

[tex]f(125) = 93.75[/tex]

Substitute 93.75 for x in g(x)

[tex]g(x) =x - 5[/tex]

[tex]g(93.75) = 93.75 - 5[/tex]

[tex]g(93.75) = 88.75[/tex]

Hence, the price of a $125 item after both price adjustments is $88.75

(d) The order of adjustment

Yes, the order in which the adjustments are applied makes a difference.

This is so because:

[tex]f(g(x)) \ne g(f(x))[/tex]

Read more about composite functions at:

https://brainly.com/question/10687170

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