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For the pair of functions f(x) and g(x), find and fully simplify the following. f(x)=3x−15 g(x)= x/3 +5

User Mantis
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1 Answer

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1. f(g(x)):
We substitute g(x) into f(x) and simplify:
f(g(x)) = f(x/3 + 5) = 3(x/3 + 5) - 15
= x + 15 - 15
= x
Therefore, f(g(x)) simplifies to just x.
2. g(f(x)):
We substitute f(x) into g(x) and simplify:
g(f(x)) = g(3x - 15) = (3x - 15)/3 + 5
= x - 5 + 5
= x
Similarly, g(f(x)) simplifies to x.
Hence, both f(g(x)) and g(f(x)) simplify to x, indicating that the composite functions are equal to the identity function f(x) = g(x) = x.
User John Woodruff
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