What is the domain of $sqrt((x+7)/(3-x))$ ?

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Answer 1 · 2017-02-16T07:31:04

The domain is $x in [-7,3[$

Let $f(x)=(x+7)/(3-x)$

To determine the domain,

What`s under the $sqrt$ sign is $>=0$ with $x!=3$

So,

$f(x)>=0$

We build a sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-7$ $color(white)(aaaaaa)$ $3$ $color(white)(aaaaaaa)$ $+oo$

$color(white)(aaaa)$ $x+7$ $color(white)(aaaaa)$ $-$ $color(white)(aaaaa)$ $+$ $color(white)(aa)$ $||$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $3-x$ $color(white)(aaaaa)$ $+$ $color(white)(aaaaa)$ $+$ $color(white)(aa)$ $||$ $color(white)(aaaa)$ $-$

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

Therefore,

$f(x)>=0$ when $x in [-7,3[$

What is the domain of sqrt((x+7)/(3-x))sqrt((x+7)/(3-x))?