Answer:
The answer is B
Step-by-step explanation:
hope that helps
Answer:
The only pair of functions that are inverses of each other are the ones for option D.
Step-by-step explanation:
Two functions, f(x) and g(x), are inverses if and only if:
f( g(x) ) = x
g( f(x) ) = x
So we need to check that with all the given options.
A)
![f(x) = \frac{x}{7} + 10 \\g(x) = 7*x - 10\\](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7Bx%7D%7B7%7D%20%2B%2010%20%5C%5Cg%28x%29%20%3D%207%2Ax%20-%2010%5C%5C)
then:
![f(g(x)) = \frac{7*x + 10}{7} -10 = x + \frac{10}{7} - 10](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%20%5Cfrac%7B7%2Ax%20%2B%2010%7D%7B7%7D%20-10%20%3D%20x%20%2B%20%5Cfrac%7B10%7D%7B7%7D%20%20-%2010)
This is clearly different than x, so f(x) and g(x) are not inverses.
B)
![f(x) = \sqrt[3]{11*x} \\g(x) = (\frac{x}{11} )^3](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5D%7B11%2Ax%7D%20%5C%5Cg%28x%29%20%3D%20%28%5Cfrac%7Bx%7D%7B11%7D%20%29%5E3)
Then:
![f(g(x)) = \sqrt[3]{11*(\frac{x}{11})^3 } = \sqrt[3]{\frac{x^3}{11^2} } = \frac{x}{11^{2/3}}](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%20%5Csqrt%5B3%5D%7B11%2A%28%5Cfrac%7Bx%7D%7B11%7D%29%5E3%20%7D%20%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7Bx%5E3%7D%7B11%5E2%7D%20%7D%20%3D%20%5Cfrac%7Bx%7D%7B11%5E%7B2%2F3%7D%7D)
This is different than x, so f(x) and g(x) are not inverses.
C)
![f(x) = \frac{7}{x} -2 \\g(x) = \frac{x + 2}{7}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B7%7D%7Bx%7D%20-2%20%5C%5Cg%28x%29%20%3D%20%5Cfrac%7Bx%20%2B%202%7D%7B7%7D)
Then:
![f(g(x)) = \frac{7}{\frac{x + 2}{7} } - 2 = \frac{7*7}{x + 2} - 2](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%20%5Cfrac%7B7%7D%7B%5Cfrac%7Bx%20%2B%202%7D%7B7%7D%20%7D%20-%202%20%3D%20%5Cfrac%7B7%2A7%7D%7Bx%20%2B%202%7D%20%20-%202)
Obviously, this is different than x, so f(x) and g(x) are not inverses.
D)
![f(x) = 9*x - 6\\g(x) = \frac{x + 6}{9}](https://tex.z-dn.net/?f=f%28x%29%20%3D%209%2Ax%20-%206%5C%5Cg%28x%29%20%3D%20%5Cfrac%7Bx%20%2B%206%7D%7B9%7D)
Then:
![f(g(x)) = 9*\frac{x + 6}{9} - 6 = x + 6 - 6 = x\\g(f(x)) = \frac{(9*x - 6) + 6}{9} = x](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%209%2A%5Cfrac%7Bx%20%2B%206%7D%7B9%7D%20%20-%206%20%3D%20x%20%2B%206%20-%206%20%3D%20x%5C%5Cg%28f%28x%29%29%20%3D%20%5Cfrac%7B%289%2Ax%20-%206%29%20%2B%206%7D%7B9%7D%20%20%3D%20x)
In this case we can conclude that f(x) and g(x) are inverses of each other.
Answer:
<u>$21.56</u>
Step-by-step explanation:
- Original price = $3.85
- Marked up by 40% = 3.85 x 1.4 = $5.39 per bottle
<u>Cost and discount of 5 bottles</u>
- Cost = 5 x 5.39 = $26.95
- Discount of 20% = 26.95 x 0.8 = <u>$21.56</u>
I think it’s 8 but unsure
Answer:
1 unit
Step-by-step explanation:
B is at -2
A is at -3
Subtract A from B
-2 - -3
-2 +3
1