f x = \sqrt[ 3 ] x
Solve for f (complex solution)
\left\{\begin{matrix}f=x^{-\frac{2}{3}}\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for f
\left\{\begin{matrix}f=\frac{1}{x^{\frac{2}{3}}}\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=f^{-\frac{3}{2}}\text{, }&arg(f^{-\frac{1}{2}})<\frac{2\pi }{3}\text{ and }f\neq 0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-\frac{1}{f^{\frac{3}{2}}}\text{; }x=\frac{1}{f^{\frac{3}{2}}}\text{, }&f>0\end{matrix}\right.
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xf=\sqrt[3]{x}
The equation is in standard form.
\frac{xf}{x}=\frac{\sqrt[3]{x}}{x}
Divide both sides by x.
f=\frac{\sqrt[3]{x}}{x}
Dividing by x undoes the multiplication by x.
f=x^{-\frac{2}{3}}
Divide \sqrt[3]{x} by x.
xf=\sqrt[3]{x}
The equation is in standard form.
\frac{xf}{x}=\frac{\sqrt[3]{x}}{x}
Divide both sides by x.
f=\frac{\sqrt[3]{x}}{x}
Dividing by x undoes the multiplication by x.
f=\frac{1}{x^{\frac{2}{3}}}
Divide \sqrt[3]{x} by x.
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