SOLUTION: Given f(x)= 3 over x(squared)-4 and g(x)= 5 over x Find the following 1. f o g 2. domain of f o g

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Question 443270: Given f(x)= 3 over x(squared)-4 and g(x)= 5 over x
Find the following
1. f o g
2. domain of f o g
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Given
f%28x%29=+3+%2F%28x%5E2-4+%29+and%0D%0A%7B%7B%7Bg%28x%29=+5%2F+x

Find the following
1. f o g
f+o+g%28x%29=f%28g%28x%29%29
f+o+g%28x%29=f%283%2F%285%2F+x%29%5E2-4%29%29
f+o+g%28x%29=f%283%2F%2825%2Fx%5E2-4%29%29
f+o+g%28x%29=f%283%2F%28%2825-4x%5E2%29%2Fx%5E2%29%29
f+o+g%28x%29=f%283x%5E2%2F%2825-4x%5E2%29%29

2. domain of f o g
restrictions:

25-4x%5E2could not be equal to 0
so, it will be 25-4x%5E2=0 for:
25-4x%5E2=0
25=4x%5E2
25%2F4=x%5E2
x=5%2F2...or...x=-5%2F2
so domain is (-infinity,-5%2F2) U (5%2F2, infinity)

+graph%28+500%2C+500%2C+-5%2C+10%2C+-5%2C+5%2C+3x%5E2%2F%2825-4x%5E2%29%29+