The equation of the image line is y= -0.5x.
When a line is reflected in a certain line, in this case the original line is reflected in the line y=-2, we simply flip it to the other side with respect to the line to which it is reflected. If you are going to graph it, you can see that the distance of the original line (y= 0.5x-4) from the line to which it is reflected (y=-2) and the distance of the reflected line (y=-0.5x) are symmetric.
![f(g(x)) = x\\g(f(x)) = x](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%20x%5C%5Cg%28f%28x%29%29%20%3D%20x)
Both functions are inverse of each other as their composition results in "x"
Step-by-step explanation:
Given functions are:
![f(x) = 3x-2\\g(x) = \frac{x+2}{3}](https://tex.z-dn.net/?f=f%28x%29%20%3D%203x-2%5C%5Cg%28x%29%20%3D%20%5Cfrac%7Bx%2B2%7D%7B3%7D)
First of all, we have to find f(g(x))
![f(g(x)) = 3g(x) -2\\=3(\frac{x+2}{3}) - 2\\=x+2-2\\=x](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%203g%28x%29%20-2%5C%5C%3D3%28%5Cfrac%7Bx%2B2%7D%7B3%7D%29%20-%202%5C%5C%3Dx%2B2-2%5C%5C%3Dx)
Now g(f(x))
![g(f(x)) = \frac{f(x)+2}{3}\\= \frac{3x-2+2}{3}\\=\frac{3x}{3}\\= x](https://tex.z-dn.net/?f=g%28f%28x%29%29%20%3D%20%5Cfrac%7Bf%28x%29%2B2%7D%7B3%7D%5C%5C%3D%20%5Cfrac%7B3x-2%2B2%7D%7B3%7D%5C%5C%3D%5Cfrac%7B3x%7D%7B3%7D%5C%5C%3D%20x)
The composition of both function gives the same answer "x" which means that both functions are the inverse of each other.
Keywords: Functions, Composition
Learn more about functions at:
#LearnwithBrainly
The sum is of n and 14 can be written as:
n+14=72