Domain of f(x)=
Question:

Domain of $f(x)=\sqrt{a^{2}-x^{2}}, a>0$ is

(a) (−aa)

(b) [−aa]

(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∈ [−aa]

$\therefore$ Domain of $f(x)$ is $[-a, a]$

Hence, the correct answer is option B.

Administrator

Leave a comment

Please enter comment.
Please enter your name.