Answer:
I provided a full answer and explaination in the picture attached. Good luck.
Answer:
1. x - 1
2. ![\sqrt{x^2-1}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2-1%7D)
Step-by-step explanation:
![f(g(x)) = \sqrt{x+1}^2 - 2\\ = x + 1 - 2\\= x - 1](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%20%5Csqrt%7Bx%2B1%7D%5E2%20-%202%5C%5C%20%3D%20x%20%2B%201%20-%202%5C%5C%3D%20x%20-%201)
![g(f(x)) =\sqrt{x^2-2+1}\\ = \sqrt{x^2-1}](https://tex.z-dn.net/?f=g%28f%28x%29%29%20%3D%5Csqrt%7Bx%5E2-2%2B1%7D%5C%5C%20%3D%20%5Csqrt%7Bx%5E2-1%7D)
We determine line m as follows:
*First, by theorem we have the following:
![m_1=-\frac{1}{m_2}](https://tex.z-dn.net/?f=m_1%3D-%5Cfrac%7B1%7D%7Bm_2%7D)
Here m1 & m2 are the slopes of two perpendicular lines. For all lines that are perpendicular that is true, so we calculate the slope of line m using the slope of the function given [Which has a slope of 7/4]:
![m_1=-\frac{1}{\frac{7}{4}}\Rightarrow m_1=-\frac{4}{7}](https://tex.z-dn.net/?f=m_1%3D-%5Cfrac%7B1%7D%7B%5Cfrac%7B7%7D%7B4%7D%7D%5CRightarrow%20m_1%3D-%5Cfrac%7B4%7D%7B7%7D)
So, the slope of line m is -4/7. Now, using this slope and the point (-1, 4) we replace in the following expression:
![y-y_1=m_1(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm_1%28x-x_1%29)
Here x1, y1 & m1 are the x-component of the point, the y-component of the point, and the slope of the line respectively, so we replace and solve for y:
![y-4=-\frac{4}{7}(x-(-1))\Rightarrow y-4=-\frac{4}{7}x-\frac{4}{7}](https://tex.z-dn.net/?f=y-4%3D-%5Cfrac%7B4%7D%7B7%7D%28x-%28-1%29%29%5CRightarrow%20y-4%3D-%5Cfrac%7B4%7D%7B7%7Dx-%5Cfrac%7B4%7D%7B7%7D)
![\Rightarrow y=-\frac{4}{7}x+\frac{24}{7}](https://tex.z-dn.net/?f=%5CRightarrow%20y%3D-%5Cfrac%7B4%7D%7B7%7Dx%2B%5Cfrac%7B24%7D%7B7%7D)
And that last function of y is the line m.
Answer:
Step-by-step explanation:
y=6x
Dozen=12
Half of a Dozen= 12/2=6
Every half dozen has to be 6 so x would denote that