Question

Find the domain of
$f\left(x\right)=\sqrt{4-9x^2}$

Answer 1

Given $f\left(x\right)=\sqrt{4-9x^2}$

$⟹4-9x^2\ge 0$

$⟹9x^2-4\le 0$

$⟹(x-\frac{3}{2})(x+\frac{3}{2})\le 0$

$⟹x\in [-3/2,3/2]$

The domain of $f\left(x\right)$ is $[-1.5,1.5]$