Answer:
(0, 1)
Step-by-step explanation:
Answer:
<em>Thus, f and g are inverse functions</em>
Step-by-step explanation:
<u>Inverse Functions</u>
If two functions f(x) and g(x) are inverses, then it follows that:
![f\circ g(x)=x](https://tex.z-dn.net/?f=f%5Ccirc%20g%28x%29%3Dx)
Or:
![g\circ f(x)=x](https://tex.z-dn.net/?f=g%5Ccirc%20%20f%28x%29%3Dx)
We are given
![\displaystyle f(x)=\frac{1}{4}x-6](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%3D%5Cfrac%7B1%7D%7B4%7Dx-6)
![g(x)=4x+24](https://tex.z-dn.net/?f=g%28x%29%3D4x%2B24)
Let's test if they are inverse functions:
![f\circ g(x)=\frac{1}{4}(4x+24)-6](https://tex.z-dn.net/?f=f%5Ccirc%20g%28x%29%3D%5Cfrac%7B1%7D%7B4%7D%284x%2B24%29-6)
Simplifying:
![f\circ g(x)=x+6-6=x](https://tex.z-dn.net/?f=f%5Ccirc%20g%28x%29%3Dx%2B6-6%3Dx)
Now find:
![\displaystyle g\circ f(x)=4\left(\frac{1}{4}x-6\right)+24](https://tex.z-dn.net/?f=%5Cdisplaystyle%20g%5Ccirc%20f%28x%29%3D4%5Cleft%28%5Cfrac%7B1%7D%7B4%7Dx-6%5Cright%29%2B24)
Operating:
![\displaystyle g\circ f(x)=x-24+24=x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20g%5Ccirc%20f%28x%29%3Dx-24%2B24%3Dx)
Thus, f and g are inverse functions
Answer:
133
Step-by-step explanation:
Answer:
3 factors ; 18 total conditions
Step-by-step explanation:
The study focuses on the 3 factirs which impacts life satisfaction. Thses factors are : Smoking ; Drinking and Partying and they constitute the 3 different factor variables in the study.
For each factor variable, each has a number of different conditions ;
For smoking : 2 conditions (smoking and not smoking)
Drinking : 3 conditions (no alcohol, 1 / day ; several per day)
Partying : 3 conditions (no partying, 1 hour of partying / day, 2 hours of partying / day)
Total number of conditions :
(2 * 3 * 3) = 18 conditions