Answer/Step-by-step explanation:
Recall: ![x^{-a} = \frac{1}{x^a}](https://tex.z-dn.net/?f=%20x%5E%7B-a%7D%20%3D%20%5Cfrac%7B1%7D%7Bx%5Ea%7D%20)
a. ![4^{-3} = \frac{1}{4^3} = \frac{1}{64}](https://tex.z-dn.net/?f=%204%5E%7B-3%7D%20%3D%20%5Cfrac%7B1%7D%7B4%5E3%7D%20%3D%20%5Cfrac%7B1%7D%7B64%7D%20)
b. ![13^{-2} = \frac{1}{13^2} = \frac{1}{169}](https://tex.z-dn.net/?f=%2013%5E%7B-2%7D%20%3D%20%5Cfrac%7B1%7D%7B13%5E2%7D%20%3D%20%5Cfrac%7B1%7D%7B169%7D%20)
c. ![(-3)^{-2} = \frac{1}{-3^2} = \frac{1}{9}](https://tex.z-dn.net/?f=%20%28-3%29%5E%7B-2%7D%20%3D%20%5Cfrac%7B1%7D%7B-3%5E2%7D%20%3D%20%5Cfrac%7B1%7D%7B9%7D%20)
No, she's not. If each energy drink's unit cost was just over $2.00, and there are 6 drinks in a pack, then that's at least $12.00 right there, but the entire 6-pack is on sale for only $2.99. She should find the correct price by dividing $2.99/6, resulting in about $0.50 per drink
Step-by-step explanation:
(20). FH= 22-15 = 7
(21). FH = 42 - 22 = 20
(22). FH = 53 - 40 = 13
Answer:
![f^{-1}(8)=\frac{3}{2}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%288%29%3D%5Cfrac%7B3%7D%7B2%7D)
Step-by-step explanation:
Given f(x)=![2x+5](https://tex.z-dn.net/?f=2x%2B5)
We have to find ![f^{-1}(8)](https://tex.z-dn.net/?f=f%5E%7B-1%7D%288%29)
In order to find
we have to make x as the subject of the formula
Let us assume f(x)=y
⇒![2x+5=y](https://tex.z-dn.net/?f=2x%2B5%3Dy)
Subtracting both sides by 5
![2x+5-5=y-5](https://tex.z-dn.net/?f=2x%2B5-5%3Dy-5)
![2x=y-5](https://tex.z-dn.net/?f=2x%3Dy-5)
Dividing both sides by 2
![\frac{2x}{2}=\frac{y-5}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B2%7D%3D%5Cfrac%7By-5%7D%7B2%7D)
⇒![x=\frac{y-5}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7By-5%7D%7B2%7D)
Now substituting y with x
we have ![f^{-1}(x)=\frac{x-5}{2}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Cfrac%7Bx-5%7D%7B2%7D)
Now ![f^{-1}(8)=\frac{8-5}{2}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%288%29%3D%5Cfrac%7B8-5%7D%7B2%7D)
=![\frac{3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D)
So option (ii) is correct