Question

Domain of √a²- b²), a>0 is​

Answer 1

$\\ \bigstar \: \underbrace\bold{\large \underline{Concept : - }}$

If a function contains a square root , set the equation Inside the square root greater or equal to zero and solve. The resulting answer is the domain.

And

If a function contains a fraction, set the denominator not equal to zero and solve. This resulting answer is the domain.

$\\ \bigstar \: \underbrace\bold{\large \underline{Solution : - }}$

Here,

We have ,$\sf f(x) = \sqrt{( {a}^{2} - {x}^{2} ) } \: (a > 0)$

$\\ \sf \: Clearly \: f(x) \: is \: defined, \: if \: a^2 -x^2 \ge 0$

$\\ \: \: \: \: \: \: \sf \: \: \longmapsto \: \: \: {x}^{2} \le {a}^{2}$

$\\ \: \: \: \: \: \: \sf \: \: \longmapsto \: \: \: - a \le x \le a$

$\\ \sf \qquad \qquad \qquad \: \because \: a > 0$

Therefore,

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mid{\overline{\underline\blue{ \: \bf{Domain \: of \: { f} \: is [-a,a] \: }}}} \mid$