Question

Find the domain and range of the following real functions:

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

• A. Domain $=[-2,2]$ and Range $=[0,2]$
• B. Domain $=[0,2]$ and Range $=[-2,2]$
• C. Domain $=[-3,3]$ and Range $=[0,3]$
• D. Domain $=[0,3]$ and Range $=[-3,3]$

Answer 1

The correct option is C Domain $=[-3,3]$ and Range $=[0,3]$

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

For existance of $f,9-x^2\ge 0$

$\Rightarrow (x-3)(x+3)\le 0$

$\Rightarrow x\in (-3,3)$

Values of $f\left(x\right)=\sqrt{9-(-3,3{)}^2}$

$=\sqrt{9-(0,9)}$

$=\sqrt{(0,9)}$

$=(0,3)$

Domain $=(-3,3)$ and Range $=(0,3)$