Question

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

• A. $(0,3)$
• B. $[0,3]$
• C. $(0,3]$
• D. $[0,3)$

Answer 1

Answer: (B)

We have, $f(x)=\sqrt{9-x^2}$
Let $y=\sqrt{9-x^2}$
$\Rightarrow y^2=9-x^2$
$\Rightarrow x^2=9-y^2$
$\Rightarrow x=\sqrt{9-y^2}$
Since, $f(x)\ge 0$
$\therefore 9-y^2\ge 0$
$\Rightarrow (3-y)(3+y)\ge 0$

$\therefore y\in [-3,3]$
But, $f(x)=\sqrt{9-x^2}$
$\therefore f(x)\in [0,3]$