Question

find domain of
$\sqrt{9 - {x}^}$
​

Answer 1

♣ Qᴜᴇꜱᴛɪᴏɴ :

$\large\boxed{\sf{\mathrm{Domain\:of\:}\:\sqrt{9-x}}}$

♣ ᴀɴꜱᴡᴇʀ :

$\large\boxed{\sf{\mathrm{Domain\:of\:}\:\sqrt{9-x}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:9\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:9]\end{bmatrix}}}$

♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

Domain definition :

The domain of a function is the set of input or argument values for which the function is real and defined

$\text { Find non - negative values for radicals: } x \leq 9$

$\sqrt{f\left(x\right)}\quad \Rightarrow \quad \:f\left(x\right)\ge 0$

$\sf{Solve\:\:9-x\ge \:0}$

$\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}$

$9-x-9\ge \:0-9$

$=-x\ge \:-9$

$=x\le \:9$

$\mathrm{The\:function\:domain}$

$\huge\boxed{\sf{x\le \:9}}$