given $f: (-1, 1] - \{0\} \to \mathbb R$ defined by $f(x) = 1/x - x$
let y $\in$ $R$, f(x) = y
I want to write $f(x)$ in terms of $y$, but I'm so stuck and don't know how to proceed. Should this be written as a piece wise function in terms of $y$?
$\endgroup$ 31 Answer
$\begingroup$If
$$y=\frac1x-x$$ then
$$x^2+yx-1=0.$$
Solve the quadratic equation for $x$.
$\endgroup$ 2
