Question

The range of the real-valued function $f\left(x\right)=\sqrt{9-x^2}$ is

• A. $[0,3]$
• B. $[-3,3]$
• C. $[-3,0]$
• D. None of these

Answer 1

The correct option is A $[0,3]$

$y=\sqrt{9-x^2}$

$y^2=9-x^2$

$x^2=9-y^2$

$x=\sqrt{9-y^2}$

Now domain is $[-3,3]$

Hence range of $f\left(x\right)$ is $[0,3]$