Question

Let \[f(x) = \frac{3x - 7}{x + 1}.\]find the range of $f$. give your answer as an interval.

Answer 1

Hello :
let : $y= \frac{3x-7}{x+1}$
calculate : x ......x ≠ -1 
$y(x+1) = 3x-7$
$yx+y =3x-7$
$yx-3x = -y-7$
$x(y-3) = -7-y$
$x = \frac{y+7}{3-y}$
the inverse function is : $g(x) = \frac{x+7}{3-x}$
domain of : g  is the range of : f
as an interval : ]-∞: 3 [U ]3;+∞[