Find the domain of real valued functions of real variable f (x) = \sqrt{ (9-x^2)}

Find the domain of real valued functions of real variable f (x) =\(\sqrt{ (9-x^2)}\)

Asked by Sakshi | 1 year ago |  97
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Class 11 Maths Relations and Functions         Add Answer

1 Answer

Solution :-

f (x) = \( \sqrt{(9-x^2)}\)

We know the square of a real number is never negative.

f (x) takes real values only when 9 – x2 ≥ 0

9 ≥ x2

x2 ≤ 9

x2 – 9 ≤ 0

x2 – 32 ≤ 0

(x + 3)(x – 3) ≤ 0

x ≥ –3 and x ≤ 3

x ∈ [–3, 3]

Domain (f) = [–3, 3]

Answered by Aaryan | 1 year ago
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