What is the domain and range of $y = \frac{x^{2} - 5 x - 6}{x^{2} - 3 x - 18}$ $y=(x^2 -5x -6) / (x^2 -3x -18)$ ?

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Answer 1 · 2018-03-17T23:23:41

The domain of the function is $x in RR-{-3}$ . The range is $y in RR-{1}$

Factorise the numerator and denominator

$y=(x^2-5x-6)/(x^2-3x-18)=((x+1)cancel(x-6))/((x+3)cancel(x-6))$

$=(x+1)/(x+3)$

The denominator is $!=0$ , therefore

$x+3!=0$ , $=>$ , $x!=-3$

The domain of the function is x in RR-{-3}

To determine the range, proceed as follows

$y=(x+1)/(x+3)$

$y(x+3)=x+1$

$yx-x=1-3y$

$x(y-1)=1-3y$

$x=(1-3y)/(y-1)$

The denominator is $!=0$

$y-1!=0$ , $=>$ , $y!=1$

The range is $y in RR-{1}$

graph{(x^2-5x-6)/(x^2-3x-18) [-16.02, 16.02, -8.01, 8.01]}

What is the domain and range of y=(x^2 -5x -6) / (x^2 -3x -18)y=x2−5x−6x2−3x−18y=(x^2 -5x -6) / (x^2 -3x -18)?