How do you find the domain and range for $y = 2/(x-1)$ ?

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Answer 1 · 2017-02-25T11:10:36

The domain of $y$ is $D_y=RR-{1}$
The range of $y$ is $R_y=RR-{0}$

As you cannot divide by $0$ , $x!=1$

The domain of $y$ is $D_y=RR-{1}$

To find the range, we need $y^-1$

$y=2/(x-1)$

$(x-1)y=2$

$xy-y=2$

$xy=y+2$

$x=(y+2)/y$

Therefore,

$y^-1=(x+2)/x$

The domain of $y^-1=RR-{0}$

This is the range of $y$

The range of $y$ is $R_y=RR-{0}$

How do you find the domain and range for y = 2/(x-1)y = 2/(x-1)?