Question

como calcular a inversa desta função
$\sqrt[3]{3 - {x}^{2} }$
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Answer 1

$y~=~\sqrt[3]{3-x^2}\\\\\\Trocando~x~por~y\\\\\\x~=~\sqrt[3]{3-y^2}\\\\\\Agora,~isolando~y\\\\\\(x)^3~=~\sqrt[3]{3-y^2}^{\,3}\\\\\\x^3~=~3-y^2\\\\\\x^3-3~=~-y^2\\\\\\-x^3+3~=~y^2\\\\\\\sqrt[2]{y^2}~=~\sqrt[2]{-x^3+3}\\\\\\\boxed{y~=~\sqrt[2]{3-x^3}}$