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Find domain and range of this real function f(x) = root under 9 - x^2 ?
Most Upvoted Answer
Find domain and range of this real function f(x) = root under 9 - x^2 ...
F(x) = √(9 - x²)
• Domain:
Since there is a square root x must be defined such that,
9 - x² ≥ 0 => 3² - x² ≥ 0
(3 - x)(3 + x) ≥ 0
(x - 3)(x + 3) ≤ 0
x € [-3,3]
• Range :
The range of f(x) can be any real number
• Domain:
Since there is a square root x must be defined such that,
9 - x² ≥ 0 => 3² - x² ≥ 0
(3 - x)(3 + x) ≥ 0
(x - 3)(x + 3) ≤ 0
x € [-3,3]
• Range :
The range of f(x) can be any real number
Community Answer
Find domain and range of this real function f(x) = root under 9 - x^2 ...
Domain and Range of f(x) = √(9-x^2)
Domain:
The domain of a function is the set of all possible values of x for which the function is defined. In this case, we need to find the values of x for which the square root of 9-x^2 is a real number.
To ensure that the square root is real, we must have 9-x^2 ≥ 0. Solving this inequality, we get:
9 - x^2 ≥ 0
x^2 ≤ 9
-3 ≤ x ≤ 3
Therefore, the domain of f(x) is [-3, 3].
Range:
The range of a function is the set of all possible values of y that the function can take. In this case, the function f(x) = √(9-x^2) can only take non-negative values, because the square root of a negative number is not a real number.
Furthermore, the maximum value of f(x) occurs when x = 0, which gives f(0) = √9 = 3. Therefore, the range of f(x) is [0, 3].
Summary:
- The domain of f(x) = √(9-x^2) is [-3, 3].
- The range of f(x) is [0, 3].
Domain:
The domain of a function is the set of all possible values of x for which the function is defined. In this case, we need to find the values of x for which the square root of 9-x^2 is a real number.
To ensure that the square root is real, we must have 9-x^2 ≥ 0. Solving this inequality, we get:
9 - x^2 ≥ 0
x^2 ≤ 9
-3 ≤ x ≤ 3
Therefore, the domain of f(x) is [-3, 3].
Range:
The range of a function is the set of all possible values of y that the function can take. In this case, the function f(x) = √(9-x^2) can only take non-negative values, because the square root of a negative number is not a real number.
Furthermore, the maximum value of f(x) occurs when x = 0, which gives f(0) = √9 = 3. Therefore, the range of f(x) is [0, 3].
Summary:
- The domain of f(x) = √(9-x^2) is [-3, 3].
- The range of f(x) is [0, 3].
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Find domain and range of this real function f(x) = root under 9 - x^2 ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Find domain and range of this real function f(x) = root under 9 - x^2 ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find domain and range of this real function f(x) = root under 9 - x^2 ?.
Find domain and range of this real function f(x) = root under 9 - x^2 ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Find domain and range of this real function f(x) = root under 9 - x^2 ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find domain and range of this real function f(x) = root under 9 - x^2 ?.
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