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प्रश्न
Find the domain and range of the following function.
f(x) = `sqrt(16 - x^2)`
उत्तर
f(x) = `sqrt(16 - x^2)`
For f to be defined,
16 – x2 ≥ 0
∴ x2 ≤ 16
∴ – 4 ≤ x < 4
∴ Domain of f = [– 4, 4]
Clearly, f(x) ≥ 0 and the value of f(x) would be maximum when the quantity subtracted from 16 is minimum i.e. x = 0
∴ Maximum value of f(x) = `sqrt(16)` = 4
∴ The range of f = [0, 4]
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