For each pair of functions, find f(g(x)) and g(f(x)). Simplify your answers.

Question

1. f(x)= 1/x-6, g(x)= 7/x+6

Answer 1

Solution:

f(x) = 1/(x-6) , g(x) = 7/(x+6)

f(g(x)) = 1 / [(7 / (x+6) -6] = 1/ [7 - 6(x+6) / ( x+6)] = (x+6) / [7 -6(x+6)] = ( x+6)/ (7-6x-36) = (x+6) / (-6x-29)

g(f(x)) = 7/ [(1/(x-6) +6] = 7/ [ 1 +6(x-6) / (x-6)] = 7(x-6) / [ 1+6(x-6)] = ( 7x - 42) / ( 1+6x-36) = (7x-42) / (6x-35)