The answer for it has to be 5 because 5*8=40 and 5*10=50 so its 5
Answer:
![f^{-1}(6) = 2](https://tex.z-dn.net/?f=f%5E%7B-1%7D%286%29%20%3D%202)
Step-by-step explanation:
Given
![f(2) = 6](https://tex.z-dn.net/?f=f%282%29%20%3D%206)
![f(3) = 7](https://tex.z-dn.net/?f=f%283%29%20%3D%207)
Required
![f^{-1}(6)](https://tex.z-dn.net/?f=f%5E%7B-1%7D%286%29)
First, we need to determine the slope of the function using;
![m = \frac{y_1 - y_2}{x_1 - x_2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_1%20-%20y_2%7D%7Bx_1%20-%20x_2%7D)
From the given parameters;
In ![f(2) = 6](https://tex.z-dn.net/?f=f%282%29%20%3D%206)
x = 2; y =6 --- Take this as x1 and y1
In ![f(3) = 7](https://tex.z-dn.net/?f=f%283%29%20%3D%207)
x = 3; y = 7 --- Take this as x2 and y2
becomes
![m = \frac{6 - 7}{2 - 3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B6%20-%207%7D%7B2%20-%203%7D)
![m = \frac{- 1}{ - 1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-%201%7D%7B%20-%201%7D)
![m = 1](https://tex.z-dn.net/?f=m%20%3D%201)
Next, we determine the equation of the function using
![y - y_1 = m(x - x_1)](https://tex.z-dn.net/?f=y%20-%20y_1%20%3D%20m%28x%20-%20x_1%29)
Substitute the values of x1,y1 and m
![y - 6 = 1(x - 2)](https://tex.z-dn.net/?f=y%20-%206%20%3D%201%28x%20-%202%29)
Open bracket
![y - 6 = x - 2](https://tex.z-dn.net/?f=y%20-%206%20%3D%20x%20-%202)
Add 6 to both sides
![y - 6 + 6 = x -2 +6](https://tex.z-dn.net/?f=y%20-%206%20%2B%206%20%3D%20x%20-2%20%2B6)
![y = x + 4](https://tex.z-dn.net/?f=y%20%3D%20x%20%2B%204)
Next is to determine the inverse function by swapping the positions of x and y
![x = y + 4](https://tex.z-dn.net/?f=x%20%3D%20y%20%2B%204)
Make y the subject of formula;
![y = x - 4](https://tex.z-dn.net/?f=y%20%3D%20x%20-%204)
Replace y with ![f^{-1}(x)](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29)
![f^{-1}(x) = x - 4](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%20x%20-%204)
Now, we can solve for ![f^{-1}(6)](https://tex.z-dn.net/?f=f%5E%7B-1%7D%286%29)
Substitute 6 for x
![f^{-1}(6) = 6 - 4](https://tex.z-dn.net/?f=f%5E%7B-1%7D%286%29%20%3D%206%20-%204)
![f^{-1}(6) = 2](https://tex.z-dn.net/?f=f%5E%7B-1%7D%286%29%20%3D%202)
You have a 2/9 chance of it being white. It is how many of that color or number over the total, so you have a 2/9 chance of it being white.