Answer: Put one dot above the number 1 on the dot plot. Put four dots above the number 2 on the dot plot. Finally, put one dot above the number 3 on the dot plot.
Step-by-step explanation:
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The value of f(g(2)) is 2.
<h3>What is function?</h3>
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The given table is
x f(x)
–6 1
–3 2
2 5
5 3
8 0
If the coordinates of a function f(x) is defined as (x,y)
then, the coordinates of inverse of f(x) is defined as (y,x).
f(g(y))= f(x) [ g(x)= (y,x)]
f(g(y))= y
So, If g(x) is the inverse of f(x), the f(g(y)) = y.
Also, we know g(x) is the inverse of f(x), then f(g(2)) = 2.
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Answer: X= -3/4, -1/2
Step-by-step explanation:
Answer:
C. ![y + \frac{1}{2} = 3(x - 2)](https://tex.z-dn.net/?f=y%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%3D%203%28x%20-%202%29)
Step-by-step explanation:
Given
![Point: (2,\frac{-1}{2})](https://tex.z-dn.net/?f=Point%3A%20%20%282%2C%5Cfrac%7B-1%7D%7B2%7D%29)
![Slope: 3](https://tex.z-dn.net/?f=Slope%3A%203)
Required
Equation of line
Let m represents the slope of the line;
m is calculated as thus
![m = \frac{y - y_1}{x - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By%20-%20y_1%7D%7Bx%20-%20x_1%7D)
![where (x_1,y_1) = (2,\frac{-1}{2})](https://tex.z-dn.net/?f=where%20%28x_1%2Cy_1%29%20%3D%20%282%2C%5Cfrac%7B-1%7D%7B2%7D%29)
![So; x_1 = 2; y_1 = \frac{-1}{2}](https://tex.z-dn.net/?f=So%3B%20x_1%20%3D%202%3B%20y_1%20%3D%20%5Cfrac%7B-1%7D%7B2%7D)
![m = 3](https://tex.z-dn.net/?f=m%20%3D%203)
By substituting the right values in the formula above;
becomes
![3 = \frac{y - \frac{-1}{2}}{x - 2}](https://tex.z-dn.net/?f=3%20%3D%20%5Cfrac%7By%20-%20%5Cfrac%7B-1%7D%7B2%7D%7D%7Bx%20-%202%7D)
Multiply both sides by ![(x - 2)](https://tex.z-dn.net/?f=%28x%20-%202%29)
![3 *(x - 2) = \frac{y - \frac{-1}{2}}{x - 2} *(x - 2)](https://tex.z-dn.net/?f=3%20%2A%28x%20-%202%29%20%3D%20%5Cfrac%7By%20-%20%5Cfrac%7B-1%7D%7B2%7D%7D%7Bx%20-%202%7D%20%2A%28x%20-%202%29)
![3 *(x - 2) = (y - \frac{-1}{2})](https://tex.z-dn.net/?f=3%20%2A%28x%20-%202%29%20%3D%20%28y%20-%20%5Cfrac%7B-1%7D%7B2%7D%29)
![3 *(x - 2) = (y + \frac{1}{2})](https://tex.z-dn.net/?f=3%20%2A%28x%20-%202%29%20%3D%20%28y%20%2B%20%5Cfrac%7B1%7D%7B2%7D%29)
![3(x - 2) = (y + \frac{1}{2})](https://tex.z-dn.net/?f=3%28x%20-%202%29%20%3D%20%28y%20%2B%20%5Cfrac%7B1%7D%7B2%7D%29)
![3(x - 2) = y + \frac{1}{2}](https://tex.z-dn.net/?f=3%28x%20-%202%29%20%3D%20y%20%2B%20%5Cfrac%7B1%7D%7B2%7D)
Reorder
![y + \frac{1}{2} = 3(x - 2)](https://tex.z-dn.net/?f=y%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%3D%203%28x%20-%202%29)
Hence, the equation that represents the line is ![y + \frac{1}{2} = 3(x - 2)](https://tex.z-dn.net/?f=y%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%3D%203%28x%20-%202%29)