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Algebra/Functions and their graphs

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Expert: - 10/25/2009


Question
for the given functions f and g, find the composite fundtions f0g and g0f and state their domains:

f(x)=2x+1
g(x)=x(squared)-3

Answer
The composite fog(x) is f(g(x)), which means take g and put it in for x in f.
The composite g0f(x) is g(f(x)), which means take f and put it in for x in g.

Here, f(x) = 2x+1 and g(x) = x²-3.

f(g(x)) = 2g(x) + 1 = 2x² - 6 + 1 = 2x² - 5.
g(f(x)) = f²(x) - 3 = (2x+1)² - 3 = 4x²+4x+1 - 3 = 4x² + 4x - 2.

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