Composite function?

[匿名]

2015-09-02 4:25 am

17.
A tree of height y meters has on average B branches, where B = y - 1. Each branch has on average n leaves, where n = 2B^2 - B. Find the average number of leaves of a tree as a function of height.

21.
The cost of producing q articles is given by the function C = f(q) = 100 + 2q
(a.) Find a formula for the inverse function.
(b.) Explain in practical terms what the inverse function tells you.

Thanks for any help!

回答 (1)

Lopez

2015-09-02 9:46 am

✔ 最佳答案

17.
n(y)
= 2B^2 - B
= 2( y - 1 )^2 - ( y - 1 )
= 2( y^2 - 2y + 1 ) - y + 1
= 2y^2 - 4y + 2 - y + 1
= 2y^2 - 5y + 3

Ans: n(y) = 2y^2 - 5y + 3

21.
(a)
C = 100 + 2q
2q = C - 100
q = (1/2)C - 50 , where C is an even integer and C ≧ 102
Ans: q = g(C) = (1/2)C - 50 , where C is an even integer and C ≧ 102

(b)
When cost C = 102 , it produce q = 1 article.
When cost C = 104 , it produce q = 2 articles.
When cost C = 106 , it produce q = 3 articles.
.........................
When cost = C , it produce q = (1/2)C - 50 articles , where C is an even integer

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