Given that f(x^2 - 2) = x + (1 / x). Find f(x).
*show working and explanation, PLS
1. You are supposed to know that $\displaystyle f(f^{-1}(x))=f^{-1}(f(x))=x$ with $\displaystyle f^{-1}(x)$ being the inverse of f(x).
2. Calculate the inverse of
$\displaystyle y = x^2-2~\implies~x=y^2-2~\implies~y=\pm\sqrt{x+2}$
3. Use the new y-term as argument on the given function:
$\displaystyle f((\sqrt{x+2})^2-2)=\sqrt{x+2}+\dfrac1{\sqrt{x+2}}$
$\displaystyle f(x)=\dfrac{(\sqrt{x+2})^2+1}{\sqrt{x+2}}=\dfrac{x +3}{\sqrt{x+2}}$