Let $f:\mathbb R\setminus \{-2\}\to \mathbb R\setminus \{4\}$ be a function defined by $f(x)=\dfrac{4x}{x+2}$. Show that $f$ is surjective.
Ok so this is a pretty straightforward question, I did the necessary steps like
Let $y\in \mathbb R\setminus\{4\}$ such that $x=\dfrac{-2y}{y-4}$. Then,
$\displaystyle f(x)=f\left(\frac{-2y}{y-4}\right)=y.$
Therefore, $f$ is surjective, as there exists an $x\in \mathbb R\setminus \{-2\}$ for all $y\in \mathbb R\setminus\{4\}$.
But my teacher said, there is another step.
Which step have I left out?