What is the range of the function $y=(x+5)/(x-2)$ ?

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What is the range of the function $y=(x+5)/(x-2)$ ?

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Answer 1 · 2016-12-24T16:23:19

$(-oo,1)(1,oo)$

Explanation:

Solve for $x$ , as follows

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

$yx -x= 2y+5$

$x(y-1)=2y+5$

$x= (2y+5)/(y-1)$

In the above expression, $x$ becomes undefined for $y=1$ . This except for $y=1$ , $x$ is defined on all the number line. Hence Range of $y$ is $(-oo,1)U(1,oo)$

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What is the range of the function $y=(x+5)/(x-2)$ ?

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What is the range of the function $y=(x+5)/(x-2)$ ?