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प्रश्न
Find the domain and range of the following real function:
f(x) = `sqrt(9 - x^2)`
उत्तर
Given:
f (x) = `sqrt{9 - x^2`
(9 - x2 ) ≥ 0
=> 9 ≥ x2
=> x ∈ [-3, 3]
`sqrt{9 - x^2` is defined for all real numbers that are greater than or equal to – 3 and less than or equal to 3.
Thus, domain of f (x) is {x : – 3 ≤ x ≤ 3} or [– 3, 3].
For any value of x such that – 3 ≤ x ≤ 3, the value of f (x) will lie between 0 and 3.
Hence, the range of f (x) is {x: 0 ≤ x ≤ 3} or [0, 3].
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