Question

domínio da função y=log(x+3) (x^2-16)

Answer 1

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$\sf{log_ba~\exists\Huge\Leftrightarrow a>0~,1\ne b>0}$

$\sf{log~_{x+3}~x^2-16}\\\sf{C.E:}\begin{cases}\sf{x^2-16>0}\\\sf{x+3>0}\\\sf{x+3\ne1}\end{cases}$

$\sf{f(x)=x^2-16}\\\sf{f(x)=0\implies x^2-16=0}\\\sf{x^2=16}\\\sf{x=\pm\sqrt{16}}\\\sf{x_1=4~~~x_2=-4}\\\sf{f(x)>0\implies x<-4~ou~x>4}\\\sf{s_1=\{x\in\mathbb{R}/x<-4~ou~x>4\}}$

$\sf{x+3>0\implies x>-3}\\\sf{x+3\ne1}\\\sf{x\ne1-3}\\\sf{x\ne-2}\\\sf{s_2=\{x\in\mathbb{R}/x>-3~e~x\ne-2\}}$

$\boxed{\boxed{\boxed{\boxed{\boxed{\sf{Dom~f(x)=\{x\in\mathbb{R}/x>-3~e~x\ne-2\}}}}}}}$