1. ## FUNction

Given that f(x^2 - 2) = x + (1 / x). Find f(x).

*show working and explanation, PLS

2. Originally Posted by mathbuoy
Given that f(x^2 - 2) = x + (1 / x). Find f(x).

*show working and explanation, PLS
1. You are supposed to know that $f(f^{-1}(x))=f^{-1}(f(x))=x$ with $f^{-1}(x)$ being the inverse of f(x).

2. Calculate the inverse of

$y = x^2-2~\implies~x=y^2-2~\implies~y=\pm\sqrt{x+2}$

3. Use the new y-term as argument on the given function:

$f((\sqrt{x+2})^2-2)=\sqrt{x+2}+\dfrac1{\sqrt{x+2}}$

$f(x)=\dfrac{(\sqrt{x+2})^2+1}{\sqrt{x+2}}=\dfrac{x +3}{\sqrt{x+2}}$