Composite Functions
posted by MV on .
f(x)=(7x+28)/(x3) and g(x)=(3x+28)/(x7)
Find: (fog)(x)
(gof)(x)
(fog)(1)

f(g) = (7g+28)/(g3)
= (7(3x+28)/(x7) + 28)/(3x+28)/(x7)  3)
= x
g(f) = (3f+28)/(f7)
= (3(7x+28)/(x3) + 28) / ((7x+28)/(x3)  7)
= x
How odd! However, if you solve for f^{1}(x) you get g(x) and viceversa.
f(g(1)) = f(1) = 1