What is the domain and range of $y= 1/(x^2-25)$ ?

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Answer 1 · 2018-03-18T08:13:51

The domain of $y$ is $x in RR-{-5,5}$ .
The range is $y in [-1/25, 0)uu(0, +oo)$

As you cannot divide by $0$ , the denominator is $!=0$

Therefore,

$x^2-25!=0$ , $=>$ $x!=-5$ and $x!=5$

The domain of $y$ is $x in RR-{-5,5}$

To calculate the range, proceed as follows

$y=1/(x^2-25)$

$y(x^2-25)=1$

$yx^2-1-25y=0$

$x^2=(1+25y)/y$

$x=sqrt((1+25y)/y)$

Therefore,

$y !=0$

and

$1+25y>=0$

$y>=-1/25$

The range is $y in [-1/25, 0)uu(0, +oo)$

graph{1/(x^2-25) [-6.24, 6.244, -3.12, 3.12]}

What is the domain and range of y= 1/(x^2-25)y= 1/(x^2-25)?