The domain of the function \(f(x) = \frac{1}{\sqrt{9-x^2}}\) is(a) –

1.	The domain of the function \(f(x) = \frac{1}{\sqrt{9-x^2}}\) is(a) – 3 ≤ x ≤ 3 (b) – 3 < x < 3 (c) – 9 ≤ x ≤ 9 (d) – ∞ < x < ∞
Answer» Answer: (a) – 3 ≤ x ≤ 3 f(x) = \(\frac{1}{\sqrt{9-x^2}}\) will be defined if 9 – x² > 0 (∵ 9 – x² ≠0) ⇒ x² – 9 < 0 ⇒ (x + 3) (x – 3) < 0 ⇒ x ∈ (– 3, 3)

The domain of the function \(f(x) = \frac{1}{\sqrt{9-x^2}}\) is(a) – 3 ≤ x ≤ 3 (b) – 3 < x < 3 (c) – 9 ≤ x ≤ 9 (d) – ∞ < x < ∞

Answer»

Answer: (a) – 3 ≤ x ≤ 3

f(x) = \(\frac{1}{\sqrt{9-x^2}}\) will be defined if 9 – x² > 0 (∵ 9 – x² ≠0)

⇒ x² – 9 < 0 ⇒ (x + 3) (x – 3) < 0

⇒ x ∈ (– 3, 3)