How to find $f(x)$ and $g(x)$ when only given $f(g(x))$ I've learned how to find $f(g(x))$ when given the two $f(x)$ and $g(x)$ functions fairly easily, but I haven't found anywhere online showing how to do the opposite. For this question I'm working on I'm asked to find $f(x)$ and $g(x)$ if $\cos^2(x) = f(g(x))$. 
Can anyone please help me figure out how to solve this? Also if someone could provide a website that helps explain this that would be greatly appreciated.

In general, you'd never be able to tell. However, there are 'more correct' answers than others. For example, you have the example 
$$
f(g(x))=\cos^2(x)
$$
Notice that this is the same as
$$
f(g(x))=\left(\cos x\right)^2
$$
So it would 'make sense' to choose $g(x)=\cos x$ and choose $f(x)=x^2$. However, There are more possible choices. For instance, choosing $g(x)=\sqrt{\cos x}$ and $f(x)=x^4$ would have also worked. 
Furthermore, take the example of 
$$
f(g(x))=x
$$
was $g(x)=2x$ and $f(x)=\frac{1}{2}x$? Or perhaps, $g(x)=\sqrt{x}$ and $f(x)=x^2$. Notice that one can uniquely determine the functions but there are smart and easy choices. It's just about choosing them 'wisely'. 
