Question

Let D be the domain of the
real valued function $f$
defined by $f\left(x\right)=\sqrt{25-x^2}$

Then, write D.

Answer 1

Given : $f\left(x\right)=\sqrt{25-x^2}$

is a real - valued , we must have
For $f\left(x\right)$ to be real - valued , we must have
$25-x^2\ge 0$
$\Rightarrow x^2\le 25$
$\Rightarrow -5\le x\le 5$
Hence, Domain $\left(D\right)=[-5,5]$