Question:
Domain of $f(x)=\sqrt{a^{2}-x^{2}}, a>0$ is
(a) (−a, a)
(b) [−a, a]
(c) [0, a]
(d) (−a, 0]
Solution:
$f(x)=\sqrt{a^{2}-x^{2}} \cdot a>0$
Since a2 − x2 ≥ 0
i.e −x2 ≥ −a2
i.e x2 ≤ a2
i.e |x| ≤ a
i.e −a ≤ x ≤ a
i.e x∈ [−a, a]
$\therefore$ Domain of $f(x)$ is $[-a, a]$
Hence, the correct answer is option B.
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