Range Math Example 2

Solution

1. 1
   Set $y = \frac{2x + 1}{x - 3}$ and solve for $x$: $y(x - 3) = 2x + 1$.
2. 2
   Expand: $yx - 3y = 2x + 1$. Collect $x$ terms: $x(y - 2) = 3y + 1$.
3. 3
   So $x = \frac{3y + 1}{y - 2}$, which is defined when $y \neq 2$.
4. 4
   The range is all real numbers except $2$: $(-\infty, 2) \cup (2, \infty)$.