# Composite Functions

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f(x)=(7x+28)/(x-3) and g(x)=(3x+28)/(x-7)

Find: (fog)(x)
(gof)(x)
(fog)(-1)

• Composite Functions -

f(g) = (7g+28)/(g-3)
= (7(3x+28)/(x-7) + 28)/(3x+28)/(x-7) - 3)
= x

g(f) = (3f+28)/(f-7)
= (3(7x+28)/(x-3) + 28) / ((7x+28)/(x-3) - 7)
= x

How odd! However, if you solve for f-1(x) you get g(x) and vice-versa.

f(g(-1)) = f(-1) = -1

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