Answer:
![f^{-1}(6) = 50](https://tex.z-dn.net/?f=f%5E%7B-1%7D%286%29%20%3D%2050)
Step-by-step explanation:
Given
![f(x) = \sqrt{2x} - 4](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%7B2x%7D%20-%204)
Required
Find ![f^{-1}(6)](https://tex.z-dn.net/?f=f%5E%7B-1%7D%286%29)
First, we calculate the inverse function
![f(x) = \sqrt{2x} - 4](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%7B2x%7D%20-%204)
Express f(x) as y
![y = \sqrt{2x} - 4](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%7B2x%7D%20-%204)
Swap the positions of x and y
![x = \sqrt{2y} - 4](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%7B2y%7D%20-%204)
Solve for y: Add 4 to both sides
![4 + x = \sqrt{2y} - 4+4](https://tex.z-dn.net/?f=4%20%2B%20x%20%3D%20%5Csqrt%7B2y%7D%20-%204%2B4)
![4 + x = \sqrt{2y}](https://tex.z-dn.net/?f=4%20%2B%20x%20%3D%20%5Csqrt%7B2y%7D)
Square both sides
![(4 + x)^2 = 2y](https://tex.z-dn.net/?f=%284%20%2B%20x%29%5E2%20%3D%202y)
Divide both sides by 2
![y = \frac{(4 + x)^2}{2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B%284%20%2B%20x%29%5E2%7D%7B2%7D)
Express y as an inverse function
![f^{-1}(x) = \frac{(4 + x)^2}{2}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%20%5Cfrac%7B%284%20%2B%20x%29%5E2%7D%7B2%7D)
Next, 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) = \frac{(4 + 6)^2}{2}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%286%29%20%3D%20%5Cfrac%7B%284%20%2B%206%29%5E2%7D%7B2%7D)
![f^{-1}(6) = \frac{(10)^2}{2}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%286%29%20%3D%20%5Cfrac%7B%2810%29%5E2%7D%7B2%7D)
![f^{-1}(6) = \frac{100}{2}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%286%29%20%3D%20%5Cfrac%7B100%7D%7B2%7D)
![f^{-1}(6) = 50](https://tex.z-dn.net/?f=f%5E%7B-1%7D%286%29%20%3D%2050)
M or the slope has to be constant throughout the graph. This is because in order for a line to be linear it has to be increasing or decreasing at the same rate. So it the slope was 2 from point x 1 -2 then the slope changed to 1 from 3-4 it would not be linear. :)
Given:7-x-5=x+2
1)combine like terms
2-x=x+2
2)Isolate the variable
-x=x+2-2
3)move x to the left
-x-x=0
4)combine like terms
-2x=0
5)Divide
X=0
Answer:
− x + 16y
Step-by-step explanation:
2x + 5y − 3x + 11y
= 2x + 5y + − 3x + 11y
Combine Like Terms:
= 2x + 5y + − 3x + 11y
= (2x + − 3x) + (5y + 11y)
= − x + 16y