If I have the follow function $ f: \mathbb{R}-\lbrace2\rbrace \rightarrow \mathbb{R} - \lbrace5\rbrace \mid f(x) = \frac{5x + 1}{x - 2}$.
Solving the equation $y = \frac{5x + 1}{x - 2}$ I arrived in $x = \frac{y - 1}{5}$ but I don't know if this is right, because when applied this in $f$ I arrived in $f(x) = \frac{5y}{y - 11}$ So I could not solve anything else.
How can I prove that she is surjective or not, if I can not think of any counterexample?
You have ;
$y =\frac{5x+1}{x-2}$
$y(x-2) =5x+1$
$yx-2y = 5x+1$
$x(y-5) =1+2y $
$\implies x = \frac{1+2y}{y-5}$
The function is surjective