Question

Determine o domínio da função f(x)=√x (x+1)( x-1)

Answer 1

$\mathrm{y=\sqrt{x(x+1)(x-1)}}\\\\ \mathrm{*\ Para\ que\ y\in\mathbb{R},\ temos\ que\ \sqrt{x}\in\mathbb{R}.\ Logo\ x(x+1)(x-1)\geq0}\\\\ \mathrm{\mathbf{i)}\ x\geq0\ \ \|\ \ \mathbf{ii)}\ x+1\geq0\ \to\ x\geq-1\ \ \|\ \ \mathbf{iii)}\ x-1\geq0\ \to\ x\geq1}\\\\ \mathrm{\{x\geq0]\cap\{x\geq-1\}\cap\{x\geq1\}=\{-1\leq x\leq0\ e\ x\geq1\}}\\\\ \boxed{\mathbf{\mathbb{D}=\{x\in\mathbb{R}\ |\ -1\leq x\leq0\ e\ x\geq1\}}}\ \ \mathrm{ou}\ \ \boxed{\mathrm{\mathbb{D}=[-1,0]\cup[1,\infty)}}$