Question

A inversa de F(x)=x^3+2

Answer 1

$\displaystyle \sf f(x) = x^3+2 \ \to\ y = x^3+2 \\\\ \underline{\begin{array}{I} \text{Para achar a inversa vamos isolar o x} \\ \text{e por fim substituir y por x e x por y} \end{array} }: \\\\\\ y=x^3+2 \\\\ x^3 = y-2 \\\\ x = \sqrt[3]{\sf y-2} \\\\ trocando\ x \ por \ y \ e\ y\ por\ x : \\\\ y = \sqrt[3]{\sf x-2} \\\\ Da{\'i}}: \\\\ \huge\boxed{\sf f^{-1}(x)=\sqrt[3]{\sf x -2} \ }\checkmark$