Question

Find the domain and range of the following real functions:
i) $f\left(x\right)=-|x|$
ii) $f\left(x\right)=\sqrt{9-x^2}$

Answer 1

i)

$f\left(x\right)=-\left|x\right|$

Range $f\in (x\le 0)or(-\infty ,0]$

Domain $x\in (-\infty <x<\infty )or(-\infty ,\infty )$

ii)

$f\left(x\right)=\sqrt{9-x^2}$

Range $(0\le f(x)\le 3)or[0,3]$

Domain $x(-3\le x\le 3)or[-3,3]$