Detection of elementary functions

Example

Let $f(x)=\sin 2x$

In this case the function is a composition of two functions:$$\begin{gathered} f(x)=\sin x \\ h(x)=2x \end{gathered}$$

The composition is: $f(x)=g(h(x))$

It is read: $f(x)$ is equal to $g$ of $h(x)$

Example

Let $f(x)=(\sin 3x{)}^2$

In this case $f(x)$ is a composition of three functions:$g(x)=x^2$, $h(x)=\sin x$, $t(x)=3x$

That is: $$\begin{gathered} h(t(x))=\sin 3x \\ f(x)=g(h(t(x)))=(\sin 3x{)}^2 \end{gathered}$$

Example

Let $f(x)=\cos x^3$

Can you already identify two elementary functions that compose $f(x)$? $$\begin{gathered} f(x)=\cos x \\ h(x)=x^3 \end{gathered}$$