Choose the correct answers: Domain of a^2-x^2 (a>0) is. - Vidyadip

MCQ

Choose the correct answers: Domain of $\sqrt{\text{a}^2-\text{x}^2}(\text{a}>0)$ is.

A
(-a, a)
✓
[-a, a]
C
[0, a]
D
(-a, 0]

✓

Answer

Correct option: B.

[-a, a]

We have $\text{f(x)}\sqrt{\text{a}^2-\text{x}^2}$
Clearly f(x) is defined, if ${\text{a}^2-\text{x}^2}\geq0$
$\Rightarrow\text{x}^2\leq\text{a}^2$
$\Rightarrow-\text{a}\leq\text{x}\leq\text{a} \ [\therefore\text{a}>0]$
$\therefore$ Domain of f is [-a, a]

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