You didn’t even post a diagram
which of the following diagram represent a relation that is not a function
Answer:
The second graph is the answer.
Euclidean geometry assumes a flat plane.
<span>So triangles for example add up to 180 degrees. </span>
<span>Non-Euclidean geometry is on curved surfaces. </span>
<span>So triangles on a sphere do not add up to 180 degrees.</span>
We are given
f(x)= ![\frac{3x-1}{x-4}](https://tex.z-dn.net/?f=%5Cfrac%7B3x-1%7D%7Bx-4%7D)
g(x)=![\frac{x+1}{x}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B1%7D%7Bx%7D)
\to find f o g, replace all the x in f(x) with g(x)
![f o g = \frac{3(\frac{x+1}{x})-1}{(\frac{x+1}{x})-4}](https://tex.z-dn.net/?f=f%20o%20g%20%3D%20%5Cfrac%7B3%28%5Cfrac%7Bx%2B1%7D%7Bx%7D%29-1%7D%7B%28%5Cfrac%7Bx%2B1%7D%7Bx%7D%29-4%7D)
= Simplify by taking least common denominator and reciprocal.
Taking the least common denominator, we get
![\frac{(\frac{2x+3}{x})}{(\frac{-3x+1}{x})}](https://tex.z-dn.net/?f=%5Cfrac%7B%28%5Cfrac%7B2x%2B3%7D%7Bx%7D%29%7D%7B%28%5Cfrac%7B-3x%2B1%7D%7Bx%7D%29%7D)
Taking reciprocal, we get
![\frac{2x+3}{x}\ast \frac{x}{-3x+1}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%2B3%7D%7Bx%7D%5Cast%20%5Cfrac%7Bx%7D%7B-3x%2B1%7D)
Simplifying the expression, we get
![f o g =\frac{2x+3}{-3x+1}](https://tex.z-dn.net/?f=f%20o%20g%20%3D%5Cfrac%7B2x%2B3%7D%7B-3x%2B1%7D)
To find the domain of a composite function, we need to find the domain of f o g and the first function i.e g(x)
To find the domain of f o g, equate the denominator to 0
![-3x+1=0](https://tex.z-dn.net/?f=-3x%2B1%3D0)
![x=\frac{1}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B3%7D)
It means, domain is all real numbers except ![x=\frac{1}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B3%7D)
Domain of g(x) is all real numbers except ![x=0](https://tex.z-dn.net/?f=x%3D0)
combined domain is ![\left ( -\infty ,0 \right )\cup \left ( 0,\frac{1}{3} \right )\cup \left ( \frac{1}{3},\infty \right )](https://tex.z-dn.net/?f=%5Cleft%20%28%20-%5Cinfty%20%2C0%20%5Cright%20%29%5Ccup%20%5Cleft%20%28%200%2C%5Cfrac%7B1%7D%7B3%7D%20%5Cright%20%29%5Ccup%20%5Cleft%20%28%20%20%5Cfrac%7B1%7D%7B3%7D%2C%5Cinfty%20%5Cright%20%29)
Answer:
$96
Step-by-step explanation: