Question

Find the domain of the real valued function of real variable:

(iii) \[f\left( x \right) = \sqrt{9 - x^2}\]

 

Answer 1

(iii) Given:

\[f\left( x \right) = \sqrt{9 - x^2}\] 

We observe that f (x) is defined for all satisfying
9 -x² ≥ 0 .
⇒ x² -9 ≤ 0
⇒ (x + 3)(x -3) ≤ 0
⇒-3 ≤ x ≤ 3
x ∈ [ -3, 3]
Hence, domain ( f ) = [-3, 3]