Given $f(x+1/x) = x^2 +1/x^2$, find $f(x)$ Given $f(x+1/x) = x^2 +1/x^2$, find $f(x)$. Please show me the way you find it.
The answer in my textbook is $f(x)=\frac{1+x^2+x^4}{x\cdot \sqrt{1-x^2}}$

Let $y=x+\frac{1}{x}$, try now to express $x$ as a function of $y$.
We have 
$$x^2-xy+1=0$$
$$x=\frac{y \pm \sqrt{y^2 -4}}{2}$$
Substitute this value for x in your expression for $f$.
$$f(y)=\left(\frac{y \pm \sqrt{y^2 -4}}{2}\right)^2+\left(\frac{2}{y \pm \sqrt{y^2 -4}}\right)^2$$
$$f(y)=y^2-2$$
