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)
Answer:
n = 3
Step-by-step explanation:
It is given that W is between X and Y. It means,
WX = WY
or
XY = WX+WY
We have, WX=6n-10, XY=17, and WY=3n
So,
17= 6n-10+3n
Adding both sides 10
17+10= 6n-10+3n+10
27=9n
n = 3
Hence, the value of n is 3.
Answer:
See step-by-step explanation.
Step-by-step explanation:
For the first question, you simply put an EMPTY circle above 2 and draw an arrow from it all the way down to -3. The reason why we put an empty circle is because there is no equal sign below it.
For the second question, you put a FILLED circle above 4 and draw an arrow from it all the way down to -3. The reason why we use a filled circle is because x is less than OR equal to 4.
Start by mult. both 0.4 and 5.12 by 100. What is 40 divided by 512?
___.078_______________
512 / 40.000
3584
-----------
4160
4096
---------
64 and so on. Calculator answer is 0.078125.