Question

Step by step of how to find f(g(x)) and g(f(x))

Answer 1

Answers:

`f(g(x)) = \sqrt[3]{(x+1)/(x^3)}\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{x}`

===============================================

Work Shown:

`f(x) = \sqrt[3]{x}\\\\\\f(g(x)) = \sqrt[3]{g(x)}\\\\\\f(g(x)) = \sqrt[3]{(x+1)/(x^3)}\\\\\\`

The idea is to replace every x with g(x). Then you'll plug in the definition of g(x).

---------------------------------

Similarly,

`g(x) = (x+1)/(x^3)\\\\\\g(f(x)) = (f(x)+1)/((f(x))^3)\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{(\sqrt[3]{x})^3}\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{x}\\\\\\`