Compositions of functions: How to assign functions $f(x), g(x)$ so that $f(g(x))=\tan(x^3) $

Question

How can we define $\tan(x^3)$ with $f(g(x))$ composite function. I tried to do it this way but it didn't work.

$$g(x)=\sin(x)/\cos(x)$$

$$f(x)=x^3$$

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Editor's note: he is trying to pick an appropriate $f$ and $g$ so that $f(g(x))$ is the desired outcome. $f$ and $g$ are not fixed

Answer 1

$f(x)=\tan(x)=\frac{\sin(x)}{\cos(x)}$ , $g(x)=x^3$ , hence $\tan(x^3)=\frac{\sin(x^3)}{\cos(x^3)}$ , hence $\tan(x^3)=f(g(x))$

Answer 2

You had the right choice of which functions to use, but you named them incorrectly. In other words,

We want $$\color{green}{f}(\color{blue}{g(x)}) = \color{green}{\tan}(\color{blue}{x^3})$$

So let's name $\color{blue}{g(x) = x^3}$, and so $\color{green}{f(x) = \tan(x)}$