How do you find the domain and range of $sqrt((13x)/((x^2)-1)$ ?

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How do you find the domain and range of $sqrt((13x)/((x^2)-1)$ ?

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Answer 1 · 2017-05-29T14:51:39

The domain is $x in (-1,0] uu (+1,+oo)$
The range is $y in [0,+oo)$

Explanation:

What's uner the $sqrt$ sign is $>=0$

So,

$(13x)/(x^2-1)>=0$

$(13x)/((x+1)(x-1))>=0$

Let $f(x)=(13x)/((x+1)(x-1))$

We can build a sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaaa)$ $-1$ $color(white)(aaaaa)$ $0$ $color(white)(aaaaaaa)$ $+1$ $color(white)(aaaa)$ $+oo$

$color(white)(aaaa)$ $x+1$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $+$ $color(white)(aaaa)$ $+$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $+$

$color(white)(aaaa)$ $x$ $color(white)(aaaaaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $-$ $color(white)(aaaa)$ $+$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $+$

$color(white)(aaaa)$ $x-1$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $-$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $+$

$color(white)(aaaa)$ $f(x)$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $+$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $+$

Therefore,

$f(x)>=0$ when $x in (-1,0] uu (+1,+oo)$

The domain is $x in (-1,0] uu (+1,+oo)$

Let,

$y=sqrt((13x)/(x^2-1))$

When $x=-1$ , $=>$ , $y=+oo$

When $x=0$ , $=>$ , $y=0$

The range is $y in [0,+oo)$

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How do you find the domain and range of $sqrt((13x)/((x^2)-1)$ ?

1 Answer

Explanation:

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How do you find the domain and range of sqrt((13x)/((x^2)-1)sqrt((13x)/((x^2)-1)?

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How do you find the domain and range of $sqrt((13x)/((x^2)-1)$ ?