How do you find the domain and range of $2/ root4(9-x^2)$ ?

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Answer 1 · 2017-12-16T15:26:02

The domain is $x in (-3,3)$ . The range is $y in [1.155, +oo)$

Let $y=2/root(4)(9-x^2)$

The denominator must be $!=0$ and $>0$

Therefore,

$9-x^2>0$

$x^2<9$

$x in (-3,3)$

The domain is $x in (-3,3)$

To find the range, proceed as follows

$y^4=16/(9-x^2)$

$9-x^2=16/y^4$

$x^2=9-16/y^4$

$x=sqrt((9y^4-16)/(y^4))$

Therefore,

$y!=0$

and

$9y^4-16>=0$

$y^4>=16/9$

$y>=2/sqrt3$

The range is $y in [2/sqrt3, +oo)$

graph{root(4)(16/(9-x^2)) [-7.02, 7.03, -2.197, 4.827]}

How do you find the domain and range of 2/ root4(9-x^2)2/ root4(9-x^2)?