Mean = 5.555555555.....
median = 6
mode = 6
range= 1
Hi there!
![\large\boxed{f^{-1}(x) = \sqrt[3]{\frac{x+4}{9} } }](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Bf%5E%7B-1%7D%28x%29%20%3D%20%20%5Csqrt%5B3%5D%7B%5Cfrac%7Bx%2B4%7D%7B9%7D%20%7D%20%7D)
![f(x) = 9x^{3} - 4](https://tex.z-dn.net/?f=f%28x%29%20%3D%209x%5E%7B3%7D%20-%204)
Find the inverse by replacing f(x) with y and swapping the x and y variables:
![x = 9y^{3} - 4](https://tex.z-dn.net/?f=x%20%3D%209y%5E%7B3%7D%20-%204)
Isolate y by adding 4 to both sides:
![x + 4 = 9y^{3}](https://tex.z-dn.net/?f=x%20%2B%204%20%3D%209y%5E%7B3%7D)
Divide both sides by 9:
![\frac{x+4}{9}= y^{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B4%7D%7B9%7D%3D%20y%5E%7B3%7D)
Take the cube root of both sides:
![y = \sqrt[3]{\frac{x+4}{9} }\\\\f^{-1}(x) = \sqrt[3]{\frac{x+4}{9} }](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7Bx%2B4%7D%7B9%7D%20%7D%5C%5C%5C%5Cf%5E%7B-1%7D%28x%29%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7Bx%2B4%7D%7B9%7D%20%7D)
Answer:15
Step-by-step explanation:
Given
Craftsman sell 10 Jewelry set for $500 each
For each additional set he will decrease the price by $ 25
Suppose he sells n set over 10 set
Earning![=\text{Price of each set}\times \text{no of set}](https://tex.z-dn.net/?f=%3D%5Ctext%7BPrice%20of%20each%20set%7D%5Ctimes%20%5Ctext%7Bno%20of%20set%7D)
Earning ![=(500-25n)(10+n)](https://tex.z-dn.net/?f=%3D%28500-25n%29%2810%2Bn%29)
![E=5000+500n-25n^2-250n](https://tex.z-dn.net/?f=E%3D5000%2B500n-25n%5E2-250n)
differentiate to get the maximum value
![\frac{dE}{dn}=-50n+250](https://tex.z-dn.net/?f=%5Cfrac%7BdE%7D%7Bdn%7D%3D-50n%2B250)
Equate
to get maximum value
![-50n+250=0](https://tex.z-dn.net/?f=-50n%2B250%3D0)
![n=\frac{250}{50}](https://tex.z-dn.net/?f=n%3D%5Cfrac%7B250%7D%7B50%7D)
![n=5](https://tex.z-dn.net/?f=n%3D5)
Thus must sell 5 extra set to maximize its earnings.
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