Find the domain of each of the following real valued functions of real

1.	Find the domain of each of the following real valued functions of real variable :f(x) = √(9-x2)
Answer» f(x) = √(9-x²) We know, The square of a real number is never negative. Clearly, 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] Thus, Domain of f = [–3, 3]

Find the domain of each of the following real valued functions of real variable :f(x) = √(9-x2)

Answer»

f(x) = √(9-x²)

We know,

The square of a real number is never negative.

Clearly,

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]

Thus,

Domain of f = [–3, 3]