The range of the function f ( x ) = 9 - x 2 is

Question

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

Smart Achievers · Accepted Answer

(1)

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

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

Clearly, $9 - y^{2} \geq 0 \Rightarrow y^{2} \leq 9 \Rightarrow - 3 \leq y \leq 3$

But $y \geq 0$ . Hence, $0 \leq y \leq 3$

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