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The range of the real-valued function f(x) = is:
Correct answer is '0,3'. Can you explain this answer?

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Given: f(x) =
Let, y2 = 9 - x2
⇒ x2 = 9 - y2
x = ...(1)
We know that for any function f(x)= ,y ≥ 0…. (A)
From equation (1).
9 − y2 ≥ 0
y2 − 9 ≤ 0
⇒ (y + 3)(y − 3) ≤ 0
⇒ −3 ≤ y ≤ 3
But from equation (A) y must be positive, then, y = [0, 3].
Range = the value of y = [0, 3]
Hence, the correct answer is [0, 3].

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The range of the real-valued function f(x) = is:Correct answer is '0,3'. Can you explain this answer? for CAT 2023 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The range of the real-valued function f(x) = is:Correct answer is '0,3'. Can you explain this answer? covers all topics & solutions for CAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The range of the real-valued function f(x) = is:Correct answer is '0,3'. Can you explain this answer?.
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Given: f(x) = Let, y2 = 9 - x2⇒ x2 = 9 - y2x = ...(1)We know that for any function f(x)= ,y ≥ 0…. (A)From equation (1).9 − y2 ≥ 0y2 − 9 ≤ 0⇒ (y + 3)(y − 3) ≤ 0⇒ −3 ≤ y ≤ 3But from equation (A) y must be positive, then, y = [0, 3].Range = the value of y = [0, 3]Hence, the correct answer is [0, 3].