Math Question
![Select the correct answer.
Consider these functions:
\[
\begin{array}{l}
f(x)=3 x^{3}+2 \\
g(x)=\sqrt[3]{\frac{x-2}{3}}
\end{array}
\]
Which statements, if any, are true about these functions?
I. The function \( f(g(x))=x \) for all real \( x \).
II. The function \( g(f(x))=x \) for all real \( x \).
III. Functions \( f \) and \( g \) are inverse functions.
A. I only
B. II only
C. I, II, and III
D. None of the statements are true.](https://d3hlidq5bf9vg0.cloudfront.net/app-server-student/2021/12/8/8b168ede-cf7f-4f54-a4ac-3e67e8eb3c90.png "Select the correct answer.
Consider these functions:
\[
\begin{array}{l}
f(x)=3 x^{3}+2 \\
g(x)=\sqrt[3]{\frac{x-2}{3}}
\end{array}
\]
Which statements, if any, are true about these functions?
I. The function \( f(g(x))=x \) for all real \( x \).
II. The function \( g(f(x))=x \) for all real \( x \).
III. Functions \( f \) and \( g \) are inverse functions.
A. I only
B. II only
C. I, II, and III
D. None of the statements are true.")
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