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JEE Previous Year Question

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

Topic: JEE PYQ

Answer: A. Full step-by-step solution below.

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

Correct answer: A

Solution

(a) : Let y = 9 - x^{2} \Rightarrow y^{2} = 9 - x^{2} \Rightarrow x^{2} = 9 - y^{2} \Rightarrow x = 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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