Question

Explicite o domínio da função f : R → R definida por:
$f(x) = \sqrt{ \frac{x - 2}{1 - x} }$
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Answer 1

$\large\boxed{\begin{array}{l}\sf f(x)=\sqrt{\dfrac{x-2}{1-x}}\\\\\sf\dfrac{x-2}{1-x}\geqslant0\\\underline{\rm fac_{\!\!,}a}\\\sf g(x)=x-2\\\underline{\rm ra\acute iz~de~g(x)}\\\sf x-2=0\implies x=2\\\sf g(x)\geqslant0\longrightarrow x \geqslant2\\\sf g(x)\leqslant0\longrightarrow x\leqslant2\\\sf h(x)=1-x\\\underline{\rm ra\acute izes~de~h(x)}\\\sf 1-x=0\\\sf x=1\\\sf h(x)>0\implies x<1\\\sf h(x)<0\implies x>1 \\\sf montando~um~quadro~sinal\\\sf e~assinalando~a~resposta~temos\\\sf S=\{x\in\mathbb{R}/1<x\leqslant2\}\end{array}}$