Question

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

Answer 1

Answers:

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

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Work Shown:

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

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

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Similarly,

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