Domain of fx - a 2- x 2- a -0 isa -a- ab -a- a-c -0- a-d -a- 0-

F(x) = nbsp;a2 x2 nbsp;; a nbsp; gt; 0 nbsp; Since a2 nbsp; minus; nbsp;x2 nbsp; ge; 0 i.e minus;x2 nbsp; ge; minus;a2 i.e nbsp; ...

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Standard XII

Mathematics

Domain

Domain of fx ...

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]

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Solution

f(x) = $\sqrt{a^{2} - x^{2}}$ ; 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]
$∴$ Domain of f (x) is [−a, a]
Hence, the correct answer is option B.

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Domain of fx=a2-x2, a>0 is (a) (−a, a) (b) [−a, a] (c) [0, a] (d) (−a, 0]

f(x) = a2-x2 ; 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] ∴ Domain of f (x) is [−a, a] Hence, the correct answer is option B.

Domain of $f (x) = \sqrt{a^{2} - x^{2}}, a > 0$ is
(a) (−a, a)
(b) [−a, a]
(c) [0, a]
(d) (−a, 0]

f(x) = $\sqrt{a^{2} - x^{2}}$ ; 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]
$∴$ Domain of f (x) is [−a, a]
Hence, the correct answer is option B.