How do you find the domain and range of $y=(2x)/(-x-5)$ ?

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Answer 1 · 2017-02-14T10:59:40

The domain of $y$ is $RR-{-5}$
The range of $y$ is $RR-{-2}$

As you cannot divide by $0$ , $-x-5!=0$

The domain of $y$ is $D_y=RR-{-5}$

To find the range, we need $f^-1(x)$

$y=2x/-x-5$

$-yx-5y=2x$

$2x+yx=-5y$

$x(y+2)=-5y$

$x=(-5y)/(y+2)$

Therefore,

$f^-1(x)=(-5x)/(x+2)$

The range of $f(x)$ is the domain of $f^-1(x)$

The range of $f(x)$ is $R_y=RR-{-2}$

How do you find the domain and range of y=(2x)/(-x-5)y=(2x)/(-x-5)?