Decomposing a composite function: $f(g(x))=\frac{x^4+x^2}{1+x^2}$, then $f$=? We have a composite function $f(g(x))=((x^4+x^2)/(1+x^2))$ and a single function $g(x)=1-x^2$. We want to know $f(1/2)$. From theory we know that $g(x)$ had been plugged in $f(x)$, but how would i find standalone $f(x)$ from here? I thought of dividing the result by $g(x)$, but that isn't true.

Alternate way to do this is to find an $x$ such that $g(x)=\frac{1}{2}$.
Since $$g(\frac{1}{\sqrt{2}}) = \frac{1}{2}$$
We have $$f(\frac{1}{2})=f(g(\frac{1}{\sqrt{2}}))=\frac{(\frac{1}{\sqrt{2}})^4+(\frac{1}{\sqrt{2}})^2}{1+(\frac{1}{\sqrt{2}})^2} = \frac{\frac{1}{4}+\frac{1}{2}}{1+\frac{1}{2}} = \frac{\frac{3}{4}}{\frac{3}{2}} = \frac{1}{2}$$
