Answer to Question #235351 in Calculus for CCW

Question

Unit 1 Review -

(2.) Find f(g(x)) and g(f(x)) given f(x)= 3x+7 and g(x)= 1/3x - 5

(show step by step)

Answer 1

$f(g(x))=f(\frac{1}{3x-5})\\ =3(\frac{1}{3x-5})+7\\ =\frac{3+21x-35}{3x-5})\\ =\frac{21x-32}{3x-5})\\ g(f(x))=g(3x+7)\\ =\frac{1}{3(3x+7)-5}\\ =\frac{1}{9x+16}$